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LOGIC 

THE THEORY OF INQUIRY 



By 
JOHN DEWEY 




NEW YORK 
HENRY HOLT AND COMPANY 



COPYRIGHT, 1938, BY 
HENRY HOLT AND COMPANY, INC. 

January, 1939 



PRINTED IN THE UNITED STATES OF AMERICA 



PREFACE 



^his book is a development of ideas regarding the nature of 
logical theory that were first presented, some forty years ago, 
in Studies in Logical Theory; that were somewhat expanded 
in Essays in Experimental Logic and were briefly summarized with 
special reference to education in Ho<w We Think. While basic 
ideas remain the same, there has naturally been considerable modi- 
fication during the intervening years. While connection with the 
problematic is unchanged, express identification of reflective 
thought with objective inquiry makes possible, I think, a mode of 
statement less open to misapprehension than were the previous 
ones. The present work is marked in particular by application of 
the earlier ideas to interpretation of the forms and formal relations 
that constitute the standard material of logical tradition. This in- 
terpretation has at the same time involved a detailed development, 
critical and constructive, of the general standpoint and its under- 
lying ideas. 

In this connection, attention is called particularly to the principle 
of the continuum of inquiry, a principle whose importance, as far as 
I am aware, only Peirce had previously noted. Application of this 
principle enables an empirical account to be given of logical forms, 
whose necessity traditional empiricism overlooked or denied while 
at the same time it proves that the interpretation of them as a priori 
is unnecessary. The connection of the principle with generalization 
in its two forms — which are systematically distinguished through- 
out the work — and with the probability coefficient of all existential 
generalizations is, I suppose, sufficiently indicated in the chapters 
devoted to these topics. The basic conception of inquiry as de- 
termination of an indeterminate situation not only enables the vexed 
topic of the relation of judgment and propositions to obtain an ob- 
jective solution, but, in connection with the conjugate relation of 
observed and conceptual material, enables a coherent account of the 
different propositional forms to be given. 

The word "Pragmatism" does not, I think, occur in the text. 



lv PREFACE 

Perhaps the word lends itself to misconception. At all events, so 
much misunderstanding and relatively futile controversy have 
gathered about the word that it seemed advisable to avoid its use. 
But in the proper interpretation of "pragmatic," namely the func- 
tion of consequences as necessary tests of the validity of proposi- 
tions, provided these consequences are operationally instituted and 
are such as to resolve the specific problem evoking the operations, 
the text that follows is thoroughly pragmatic. 

In the present state of logic, the absence of any attempt at sym- 
bolic formulation will doubtless cause serious objection in the minds 
of many readers. This absence is not due to any aversion to such 
formulation. On the contrary, I am convinced that acceptance of 
the general principles set forth will enable a more complete and con- 
sistent set of symbolizations than now exists to be made. The ab- 
sence of symbolization is due, first, to a point mentioned in the text, 
the need for development of a general theory of language in which 
form and matter are not separated; and, secondly, to the fact that 
an adequate set of symbols depends upon prior institution of valid 
ideas of the conceptions and relations that are symbolized. With- 
out fulfilment of this condition, formal symbolization will (as 
so often happens at present) merely perpetuate existing mistakes 
while strengthening them by seeming to give them scientific stand- 
ing. 

Readers not particularly conversant with contemporary logical 
discussions may find portions of the text too technical, especially 
perhaps in Part III. I suggest that such readers interpret what is 
said by calling to mind what they themselves do, and the way they 
proceed in doing it, when they are confronted with some question 
or difficulty which they attempt to cope with in an intellectual 
way. If they pursue this course, I think the general principles will 
be sufficiently intelligible so that they will not be unduly troubled 
by technical details. It is possible that the same advice is applicable 
in the case of those whose very familiarity with current logical 
literature constitutes an obstruction to understanding a positionthat 
is at odds with most current theory. 

As far as logical treatises and their authors are concerned, I hope 
the work itself affords sufficient indication of my chief lines of in- 
debtedness. I should however state explicitly that, with the out- 
standing exception of Peirce, I have learned most from writers 
with whose positions I have in the end been compelled to disagree. 
Since it happens that there is no reference in the text to the writings 



PREFACE v 

of A. F. Bentley, I wish to record here how much I owe to them. 
My indebtedness to George H. Mead is also much greater than 
is indicated by the text. 

With emphatic repetition of the disclaimer that is usual in the 
case of personal acknowledgments of indebtedness, it is a pleasure 
to mention some of them — my obligation to a succession of students 
for a period of more than a generation in which I have lectured on 
the themes of this volume can only be stated in this general way. 
Dr. Sidney Hook has read the several versions of all the chapters of 
this book and I have profited immensely by his suggestions and 
criticisms, both as to manner and substance of what was contained 
in these chapters. Dr. Joseph Ratner read many of the chapters and 
I am also indebted to him for suggestions and corrections. In some 
of the more technical chapters I have availed myself freely of the 
superior knowledge and competency of Dr. Ernest Nagel. It is my 
fault, not his, if avoidable errors still exist in the chapters referred to. 

In conclusion, I want to say that the treatise that follows is intro- 
ductory. It is a presentation of a point of view and method of ap- 
proach. Although the statement of them has been maturing for 
over forty years, I am well aware that the presentation does not 
have and could not have the finish and completeness that are 
theoretically possible. But I am also convinced that the standpoint 
is so thoroughly sound that those who are willing to entertain it 
will in the coming years develop a theory of logic that is in thorough 
accord with all the best authenticated methods of attaining knowl- 
edge. My best wishes as well as my hopes are with those who en- 
gage in the profoundly important work of bringing logical theory 
into accord with scientific practice, no matter how much their 
conclusions may differ in detail from those presented in this book. 

J.D. 

Hubbards, Nova Scotia 
August 24, 1938 



CONTENTS 



PART 1 

INTRODUCTION 

I THE PROBLEM OF LOGICAL SUBJECT- 
MATTER 1 

II THE EXISTENTIAL MATRIX OF INQUIRY: 

BIOLOGICAL 23 

III THE EXISTENTIAL MATRIX OF INQUIRY: 

CULTURAL 42 

IV COMMON SENSE AND SCIENTIFIC INQUIRY 60 
V THE NEEDED REFORM OF LOGIC . . 81 

PART II 

THE STRUCTURE OF INQUIRY AND THE 
CONSTRUCTION OF JUDGMENTS 

VI THE PATTERN OF INQUIRY . . . . 101 

VII THE CONSTRUCTION OF JUDGMENT . . 120 

VIII IMMEDIATE KNOWLEDGE: UNDERSTAND- 
ING AND INFERENCE 139 

IX JUDGMENTS OF PRACTICE: EVALUATION 159 

X AFFIRMATION AND NEGATION: JUDG- 
MENT AS REQUALIFICATION . . . 181 

XI THE FUNCTION OF PROPOSITIONS OF 

QUANTITY IN JUDGMENT . . . . 199 



vm CONTENTS 

XII JUDGMENT AS SPATIAL-TEMPORAL DETER- 
MINATION: NARRATION-DESCRIPTION . 220 

XIII THE CONTINUUM OF JUDGMENT: 

GENERAL PROPOSITIONS .... 245 

XIV GENERIC AND UNIVERSAL PROPOSITIONS . 264 



PART III 
PROPOSITIONS AND TERMS 

XV GENERAL THEORY OF PROPOSITIONS . . 283 

XVI PROPOSITIONS ORDERED IN SETS AND 

SERIES 311 

XVII FORMAL FUNCTIONS AND CANONS . . 328 

XVIII TERMS OR MEANINGS 349 

PART IV 

THE LOGIC OF SCIENTIFIC METHOD 

XIX LOGIC AND NATURAL SCIENCE: FORM AND 

MATTER 371 

XX MATHEMATICAL DISCOURSE .... 394 

XXI SCIENTIFIC METHOD: INDUCTION AND 

DEDUCTION 419 

XXII SCIENTIFIC LAWS— CAUSATION AND 

SEQUENCES 442 

XXIII SCIENTIFIC METHOD AND SCIENTIFIC 

SUBJECT-MATTER 463 

XXIV SOCIAL INQUIRY 487 

XXV THE LOGIC OF INQUIRY AND PHILOSOPHIES 

OF KNOWLEDGE 513 



Part One 

INTRODUCTION: THE MATRIX OF INQUIRY 



CHATTER I 

THE PROBLEM OF LOGICAL 
SUBJECT-MATTER 



Contemporary logical theory is marked by an apparent 
paradox. There is general agreement as to its proximate 
subject-matter. With respect to this proximate subject- 
matter no period shows a more confident advance. Its ultimate 
subject-matter, on the other hand, is involved in controversies 
which show little sign of abating. Proximate subject-matter is the 
domain of the relations of propositions to one another, such as 
affirmation-negation, inclusion-exclusion, particular-general, etc. 
No one doubts that the relations expressed by such words as is, is- 
not, if -then, only (none but), and, or, some-all, belong to the 
subject-matter of logic in a way so distinctive as to mark off a 
special field. 

When, however, it is asked how and why the matters designated 
by these terms form the subject-matter of logic, dissension takes 
the place of consensus. Do they stand for pure forms, forms that 
have independent subsistence, or are the forms in question forms 
of subject-matter? If the latter, what is that of which they are 
forms, and what happens when subject-matter takes on logical 
form? How and why? 

These are questions of what I called the ultimate subject-matter 
of logic; and about this subject-matter controversy is rife. Un- 
certainty about this question does not prevent valuable work in 
the field of proximate subject-matter. But the more developed 
this field becomes, the more pressing is the question as to what it is 
all about. Moreover, it is not true that there is complete agreement 
in the more limited field. On the contrary, in some important 
matters, there is conflict even here; and there is a possibility (which 

1 



2 INTRODUCTION: THE MATRIX OF INQUIRY 

will be shown in the sequel to be actualized) that the uncertainty 
and diversity that exists in the limited field is a reflection of the 
unsettled state of opinion about ultimate subject-matter. 

To illustrate the existing uncertainty as to ultimate subject- 
matter, it is only necessary to enumerate some of the diverse con- 
ceptions about the nature of logic that now stand over against 
one another. It is said, for example, that logic is the science of 
necessary laws of thought, and that it is the theory of ordered 
relations— relations which are wholly independent of thought. 
There are at least three views held as to the nature of these latter 
relations: They are held (1) to constitute a realm of pure pos- 
sibilities as such, where pure means independent of actuality; (2) 
to be ultimate invariant relations forming the order of nature; 
and (3) to constitute the rational structure of the universe. In 
the latter status, while independent of human thought, they are 
said to embody the rational structure of the universe which is re- 
produced in part by human reason. There is also the view that 
logic is concerned with processes of inference by which knowl- 
edge, especially scientific knowledge, is attained. 

Of late, another conception of its subject-matter has appeared 
upon the scene. Logic is said to be concerned with the formal 
structure of language as a system of symbols. And even here 
there is division. Upon one view, logic is the theory of trans- 
formation of linguistic expressions, the criterion of transformation 
being identity of syntactical forms. According to another view, 
the symbolic system, which is the subject-matter of logic, is a 
universal algebra of existence. 

In any case, as regards ultimate subject-matter, logic is a branch 
of philosophic theory; so that different views of its subject-matter 
are expressions of different ultimate philosophies, while logical con- 
clusions are used in turn to support the underlying philosophies. 
In view of the fact that philosophizing must satisfy logical re- 
quirements there is something in this fact that should at least pro- 
voke curiosity; conceivably it affects unfavorably the autonomy of 
logical theory. On the face of the matter, it does not seem fitting 
that logical theory should be determined by philosophical realism 
or idealism, rationalism or empiricism, dualism or monism, atomistic 
or organic metaphysics. Yet even when writers on logic do not 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 3 

express their philosophic prepossessions, analysis discloses a connec- 
tion. In some cases conceptions borrowed from one or another 
philosophic system are openly laid down as -foundations of logic 
and even of mathematics. 

This list of diverse views given above is put down by way of 
illustration. It is not exhaustive, but it suffices to justify one more 
endeavor to deal with proximate subject-matter in terms of a 
theory concerning the ultimate subject-matter of logic. In the 
present state of affairs, it is foolish to say that logic must be about 
this or that. Such assertions are verbal realisms, assuming that a 
word has such magical power that it can point to and select the 
subject to which it is applicable. Furthermore, any statement that 
logic is so-and-so, can, in the existing state of logical theory, be 
offered only as a hypothesis and an indication of a position to be 
developed. 

Whatever is offered as a hypothesis must, however, satisfy cer- 
tain conditions. It must be of the nature of a vera causa. Being a 
vera causa, does not mean, of course, that it is a true hypothesis, 
for if it were that, it would be more than a hypothesis. It means 
that whatever is offered as the ground of a theory must possess the 
property of verifiable existence in some domain, no matter how 
hypothetical it is in reference to the field in which it is proposed 
to apply it. It has no standing if it is drawn from the void and 
proffered simply ad hoc. The second condition that a hypothesis 
about ultimate logical subject-matter must satisfy is that it be able 
to order and account for what has been called the proximate 
subject-matter. If it cannot meet the test thus imposed, no amount 
of theoretical plausibility is of avail. In the third place, the 
hypothesis must be such as to account for the arguments that are 
advanced in support of other theories. This condition corresponds 
to the capacity of a theory in any field to explain apparent negative 
cases and exceptions. Unless this condition is fulfilled, conclusions 
reached in satisfaction of the second condition are subject to the 
fallacy of affirming an antecedent clause because the consequent is 
affirmed. 

From these preliminary remarks I turn to statement of the posi- 
tion regarding logical subject-matter that is developed in this work. 
The theory, in summary form, is that all logical forms (with their 



4 INTRODUCTION: THE MATRIX OF INQUIRY 

characteristic properties) arise within the operation of inquiry and 
are concerned with control of inquiry so that it may yield 
warranted assertions. This conception implies much more than 
that logical forms are disclosed or come to light when we reflect 
upon processes of inquiry that are in use. Of course it means that; 
but it also means that the forms originate in operations of inquiry. 
To employ a convenient expression, it means that while inquiry into 
inquiry is the causa cognoscendi of logical forms, primary inquiry 
is itself causa essendi of the forms which inquiry into inquiry dis- 
closes. 

It is not the task of this chapter to try to justify this hypothesis, 
or to show that it satisfies the three conditions laid down. That 
is the business of the work as a whole. But I wish to emphasize 
two points preparatory to expounding the meaning (not the 
justification) of the conception, an exposition that is the main task 
of the present chapter. One of them is that any revulsion against 
the position just indicated should be tempered by appreciation of 
the fact that all other conceptions of logical subject-matter that 
are now entertained are equally hypothetical. If they do not seem 
to be so, it is because of their familiarity. If sheer dogmatism is 
to be avoided, any hypothesis, no matter how unfamiliar, should 
have a fair chance and be judged by its results. The other point 
is that inquiries, numerous in variety and comprehensive in scope, 
do exist and are open to public examination. Inquiry is the life- 
blood of every science and is constantly engaged in every art, 
craft and profession. In short, the hypothesis represents a vera 
causa, no matter what doubt may attend its applicability in the 
field of logic. 

Further elucidation of the meaning of the position taken will 
proceed largely in terms of objections that are most likely to arise. 
The most basic of these objections is that the field indicated, that 
of inquiries, is already pre-empted. There is, it will be said, a 
recognized subject which deals with it. That subject is method- 
ology; and there is a well recognized distinction between method- 
ology and logic, the former being an application of the latter. 

It certainly cannot be shown, short of the total development of 
the position taken, that this objection is not just. But it may be 
noted that assertion in advance of a fixed difference between logic 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 5 

and the methodology of scientific and practical inquiry begs the 
fundamental question at issue. The fact that most of the extant 
treatises upon methodology have been written upon the assump- 
tion of a fixed difference between the two does not prove that the 
difference exists. Moreover, the relative failure of works on logic 
that have identified logic and methodology (I may cite the logic 
of Mill as an example) does not prove that the identification is 
doomed to failure. For the failure may not be inherent. In any 
case, a priori assumption of a dualism between logic and method- 
ology can only be prejudicial to unbiased examination both of 
methods of inquiry and logical subject-matter. 

The plausibility of the view that sets up a dualism between 
logic and the methodology of inquiry, between logic and scien- 
tific method, is due to a fact that is not denied. Inquiry in order to 
reach valid conclusions must itself satisfy logical requirements. 
It is an easy inference from this fact to the idea that the logical re- 
quirements are imposed upon methods of inquiry from without. 
Since inquiries and methods are better and worse, logic involves a 
standard for criticizing and evaluating them. How, it will be 
asked, can inquiry which has to be evaluated by reference to a 
standard be itself the source of the standard? How can inquiry 
originate logical forms (as it has been stated that it does) and yet 
be subject to the requirements of these forms? The question is 
one that must be met. It can be adequately answered only in the 
course of the entire discussion that follows. But the meaning of 
the position taken may be clarified by indicating the direction in 
which the answer will be sought. 

The problem reduced to its lowest terms is whether inquiry can 
develop in its own ongoing course the logical standards and forms 
to which further inquiry shall submit. One might reply by say- 
ing that it can because it has. One might even challenge the ob- 
jector to produce a single instance of improvement in scientific 
methods not produced in and by the self-corrective process of 
inquiry; a single instance that is due to application of standards ab 
extra. But such a retort needs to be justified. Some kind of inquiry 
began presumably as soon as man appeared on earth. Of prehis- 
toric methods of inquiry our knowledge is vague and speculative. 
But we know a good deal about different methods that have been 



6 INTRODUCTION: THE MATRIX OF 1XQUIRY 

used in historic times. We know that the methods which now 
control science are of comparatively recent origin in both physical 
and mathematical science. 

Moreover, different methods have been not only tried, but they 
have been tried out; that is, tested. The developing course of 
science thus presents us with an immanent criticism of methods 
previously tried. Earlier methods failed in some important respect. 
In consequence of this failure, they were modified so that more 
dependable results were secured. Earlier methods yielded con- 
clusions that could not stand the strain put upon them by further 
investigation. It is not merely that conclusions were found to be 
inadequate or false but that they were found to be so because of 
methods employed. Other methods of inquiry were found to be 
such that persistence in them not only produced conclusions that 
stood the strain of further inquiry but that tended to be self-recti- 
fying. They were methods that improved with and by use. 

It may be instructive to compare the improvement of scientific 
methods within inquiry with the improvement that has taken 
place in the progress of the arts. Is there any reason to suppose 
that advance in the art of metallurgy has been due to application 
of an external standard? The "norms" used at present have de- 
veloped out of the processes by which metallic ores were formerly 
treated. There were needs to be satisfied; consequences to be 
reached. As they were reached, new needs and new possibilities 
opened to view and old processes were re-made to satisfy them. In 
short, some procedures worked; some succeeded in reaching the 
end intended; others failed. The latter were dropped; the former 
were retained and extended. It is quite true that modern improve- 
ments in technologies have been determined by advance in mathe- 
matics and physical science. But these advances in scientific 
knowledge are not external canons to which the arts have had 
automatically to submit themselves. The}' provided new instru- 
mentalities, but the instrumentalities were nor self-applying. They 
were used; and it was the result of their use, their failure'and suc- 
cess in accomplishing ends and effecting consequences, that pro- 
vided the final criterion of the value of scientific principles for 
carrying on determinate technological operations. What is said 
is not intended as proof that the logical principles involved in 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 7 

scientific method have themselves arisen in the progressive course 
of inquiry. But it is meant to show that the hypothesis that they 
have so arisen has a prima -facie claim to be entertained, final de- 
cision being reserved. 

I now return to exposition of the meaning of the position taken. 
That inquiry is related to doubt will, I suppose, be admitted. 
The admission carries with it an implication regarding the end of 
inquiry: end in both senses of the word, as end-in-view and as close 
or termination. If inquiry begins in doubt, it terminates in the 
institution of conditions which remove need for doubt. The latter 
state of affairs may be designated by the words belief and knowl- 
edge. For reasons that I shall state later I prefer the words "war- 
ranted assertibility." 

Belief may be so understood as to be a fitting designation for 
the outcome of inquiry. Doubt is uneasy; it is tension that finds 
expression and outlet in the processes of inquiry. Inquiry termi- 
nates in reaching that which is settled. This settled condition 
is a demarcating characteristic of genuine belief. In so far, be- 
lief is an appropriate name for the end of inquiry. But belief is 
a "double-barreled" word. It is used objectively to name what 
is believed. In this sense, the outcome of inquiry is a settled ob- 
jective state of affairs, so settled that we are ready to act upon it, 
overtly or in imagination. Belief here names the settled condition 
of objective subject-matter, together with readiness to act in a 
given way when, if, and as, that subject-matter is present in 
existence. But in popular usage, belief also means a personal mat- 
ter; something that some human being entertains or holds; a 
position, which under the influence of psychology, is converted 
into the notion that belief is merely a mental or psychical state. 
Associations from this signification of the word belief are likely 
to creep in when it is said that the end of inquiry is settled belief. 
The objective meaning of subject-matter as that is settled through 
inquiry is then dimmed or even shut out. The ambiguity of the 
word thus renders its use inadvisable for the purpose in hand. 

The word knowledge is also a suitable term to designate the 
objective and close of inquiry. But it, too, suffers from ambiguity. 
When it is said that attainment of knowledge, or truth, is the end 
of inquiry the statement, according to the position here taken, is 



8 INTRODUCTION: THE MATRIX OF INQUIRY 

a truism. That which satisfactorily terminates inquiry is, by 
definition, knowledge; it is knowledge because it is the appropriate 
close of inquiry. But the statement may be supposed, and has been 
supposed, to enunciate something significant instead of a tautology. 
As a truism, it defines knowledge as the outcome of competent and 
controlled inquiry. When, however, the statement is thought to 
enunciate something significant, the case is reversed. Knowledge 
is then supposed to have a meaning of its own apart from connec- 
tion with and reference to inquiry. The theory of inquiry is then 
necessarily subordinated to this meaning as a fixed external end. 
The opposition between the two views is basic. The idea that 
any knowledge in particular can be instituted apart from its being 
the consummation of inquiry, and that knowledge in general can 
be defined apart from this connection is, moreover, one of the 
sources of confusion in logical theory. For the different varieties 
of realism, idealism and dualism have their diverse conceptions of 
what "knowledge" really is. In consequence, logical theory is 
rendered subservient to metaphysical and epistemological precon- 
ceptions, so that interpretation of logical forms varies with under- 
lying metaphysical assumptions. 

The position here taken holds that since every special case of 
knowledge is constituted as the outcome of some special inquiry, 
the conception of knowledge as such can only be a generalization 
of the properties discovered to belong to conclusions which are 
outcomes of inquiry. Knowledge, as an abstract term, is a name 
for the product of competent inquiries. Apart from this relation, 
its meaning is so empty that any content or filling may be arbitra- 
rily poured in. The general conception of knowledge, when for- 
mulated in terms of the outcome of inquiry, has something im- 
portant to say regarding the meaning of inquiry itself. For it 
indicates that inquiry is a continuing process in even' field with 
which it is engaged. The "settlement" of a particular situation by 
a particular inquiry is no guarantee that that settled conclusion will 
always remain settled. The attainment of settled beliefs is a 
progressive matter; there is no belief so settled as not to be ex- 
posed to further inquiry. It is the convergent and cumulative 
effect of continued inquiry that defines knowledge in its general 
meaning. In scientific inquiry, the criterion of what is taken to be 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 9 

settled, or to be knowledge, is being so settled that it is available as 
a resource in further inquiry; not being settled in such a way as 
not to be subject to revision in further inquiry. 

What has been said helps to explain why the term "warranted 
assertion" is preferred to the terms belief and knowledge. It is free 
from the ambiguity of these latter terms, and it involves reference 
to inquiry as that which warrants assertion. When knowledge is 
taken as a general abstract term related to inquiry in the abstract, 
it means "warranted assertibility." The use of a term that desig- 
nates a potentiality rather than an actuality involves recognition 
that all special conclusions of special inquiries are parts of an 
enterprise that is continually renewed, or is a going concern. 1 

Up to this point, it may seem as if the criteria that emerge from 
the processes of continuous inquiry were only descriptive, and in 
that sense empirical. That they are empirical in one sense of that 
ambiguous word is undeniable. They have grown out of the 
experiences of actual inquiry. But they are not empirical in the 
sense in which "empirical" means devoid of rational standing. 
Through examination of the relations which exist between means 
(methods) employed and conclusions attained as their consequence, 
reasons are discovered why some methods succeed and other 
methods fail. It is implied in what has been said (as a corollary of 
the general hypothesis) that rationality is an affair of the relation 
of means and consequences, not of fixed first principles as ultimate 
premises or as contents of what the Neo-scholastics call crite- 
riology. 

Reasonableness or rationality is, according to the position here 
taken, as well as in its ordinary usage, an affair of the relation of 
means and consequences. In framing ends-in-view, it is un- 
reasonable to set up those which have no connection with available 
means and without reference to the obstacles standing in the way of 

*C. S. Peirce, after noting that our scientific propositions are subject to being 
brought in doubt by the results of further inquiries, adds, "We ought to construct 
our theories so as to provide for such [later] discoveries ... by leaving room 
for the modifications that cannot be foreseen but which are pretty sure to prove 
needful." (Collected Papers, Vol. V., p. 376 n.) The readers who are acquainted 
with the logical writings of Peirce will note my great indebtedness to him in the 
general position taken. As far as I am aware, he was the first writer on logic to 
make inquiry and its methods the primary and ultimate source of logical subject- 
matter. 



10 



INTRODUCTION: THE MATRIX OF INQUIRY 



attaining the end. It is reasonable to search for and select the 
means that will, with the maximum probability, yield the con- 
sequences which are intended. It is highly unreasonable to cm- 
ploy as means, materials and processes which would be found, if 
they were examined, to be such that they produce consequences 
which are different from the intended end; so different that they 
preclude its attainment. Rationality as an abstract conception is 
precisely the generalized idea of the means-consequence relation 
as such. Hence, from this point of view, the descriptive state- 
ment of methods that achieve progressively stable beliefs, or war- 
ranted assertibility, is also a rational statement in case the relation 
between them as means and assertibility as consequence is ascer- 
tained. 

Reasonableness or rationality has, however, been hypostatized. 
One of the oldest and most enduring traditions in logical theory 
has converted rationality into a faculty which, when it is actualized 
in perception of first truths, was called reason and later, Intcllectus 
Purus. The idea of reason as the power which intuitively appre- 
hends a priori ultimate first principles persists in logical philosophy. 
Whether explicitly affirmed or not, it is the ground of even' view 
which holds that scientific method is dependent upon logical forms 
that are logically prior and external to inquiry. The original 
ground for this conception of reason has now been destroyed. 
This ground was the necessity for postulating a faculty that had 
the power of direct apprehension of "truths" that were axiomatic 
in the sense of being self-evident, or self-verifying, and self- 
contained, as the necessary grounds of all demonstrative reasoning. 
The notion was derived from the subject-matter that had attained 
the highest scientific formulation at the time the classic logic was 
formulated; namely, Euclidean geometry. 

This conception of the nature of axioms is no longer held in 
mathematics nor in the logic of mathematics. Axioms are now 
held to be postulates, neither true nor false in themselves, and 
to have their meaning determined by the consequences that follow 
because of their implicatory relations to one another. The greatest 
freedom is permitted, or rather encouraged, in laying" down 
postulates— a freedom subject only to the condition that\hey be 
rigorously fruitful of implied consequences. 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 11 

The same principle holds in physics. Mathematical formulae 
have now taken the place in physics once occupied by proposi- 
tions about eternal essences and the fixed species defined by these 
essences. The formulae are deductively developed by means of 
rules of implication. But the value of the deduced result for 
physical science is not determined by the correctness of the deduc- 
tion. 

The deductive conclusion is used to instigate and direct opera- 
tions of experimental observation. The observable consequences 
of these operations in their systematic correlation with one an- 
other finally determine the scientific worth of the deduced 
principle. The latter takes its place as a means necessary to obtain 
the consequence of warranted assertibility. The position here 
taken, the general hypothesis advanced, is a generalization of the 
means-consequence relation characteristic of mathematical and 
physical inquiry. According to it, all logical forms, such as are 
represented by what has been called proximate logical subject- 
matter, are instances of a relation between means and consequences 
in properly controlled inquiry, the word "controlled" in this 
statement standing for the methods of inquiry that are developed 
and perfected in the processes of continuous inquiry. In this 
continuity, the conclusions of any special inquiry are subordinate 
to use in substantiation and maturation of methods of further in- 
quiry. The general character of knowledge as an abstract term 
is determined by the nature of the methods used, not vice-versa. 

The character of the generalization of the relation of "first 
principles" and conclusions (in mathematical and physical science) 
may be illustrated by the meaning of first principles in logic; such 
as traditionally represented by the principles, say, of identity, 
contradiction and excluded middle. According to one view, such 
principles represent ultimate invariant properties of the objects 
with which methods of inquiry are concerned, and to which in- 
quiry must conform. According to the view here expressed, they 
represent conditions which have been ascertained during the con- 
duct of continued inquiry to be involved in its own successful 
pursuit. The two statements may seem to amount to the same 
thing. Theoretically, there is a radical difference between them. 
For the second position implies, as has already been stated, that the 



1 2 INTRODUCTION: THE MATRIX OF INQUIRY 

principles are generated in the very process of control of continued 
inquiry, while, according to the other view, they arc a priori 
principles fixed antecedently to inquiry and conditioning it ah 

extra. 2 

Neither the existence nor the indispensability of primary logical 
principles is, then, denied. The question concerns their origin and 
use. In what is said upon this matter I follow in the main the 
account given by Peirce of "guiding" or "leading 1 ' principles. 
According to this view, every inferential conclusion that is drawn 
involves a habit (either by way of expressing it or initiating it) 
in the organic sense of habit, since life is impossible without ways 
of action sufficiently general to be properly named kihits. At the 
outset, the habit that operates in an inference is purely biological. 
It operates without our being aware of it. We are aware at most 
of particular acts and particular consequences. Later, we are 
aware not only of 'what is done from time to time but of boz? it is 
done. Attention to the way of doing is, moreover, indispensable 
to control of what is done. The craftsman, for example, learns 
that if he operates in a certain ii\iy the result will take care of it- 
self, certain materials being given. In like fashion, we discover 
that if we draw our inferences in a certain way, we shall, other 
things being equal, get dependable conclusions. The iJca of a 
method of inquiry arises as an articulate expression of the habit 
that is involved in a class of inferences. 

Since, moreover, the habits that operate are narrower and wider 
in scope, the formulations of methods that result from observing 
them have either restricted or extensive breadth. Peirce illustrates 
the narrower type of habit by the following case: A person has 
seen a rotating disk of copper come to rest when it is placed be- 
tween magnets. He infers that another piece of copper will be- 
have similarly under like conditions. At first such inferences 
are made without formulation of a principle/' The disposition that 
operates is limited in scope. It docs not extend beyond pieces of 
copper. But when it is found that there are habits involved in 

2 This point is discussed in Ch. XVII. 

3 1 do not recall that Peirce alludes to Hume's doctrine of habit, or t<» Mill's 
"propensity" to generalize. The fact involved seems to be die same. Bur Peirce 
connects the fact, as Hume and Mill did nor, with basic uremic or biological 
functions instead of leaving habit as an ultimate "mysterious" tie. 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 13 

every inference, in spite of differences of subject-matter, and 
when these habits are noted and formulated, then the formulations 
are guiding or leading principles. The principles state habits 
operative in every inference that tend to yield conclusions that are 
stable and productive in further inquiries. Being free from con- 
nection with any particular subject-matter, they are formal, not 
material, though they are forms of material that is subjected to 
authentic inquiry. 

Validity of the principles is determined by the coherency of the 
consequences produced by the habits they articulate. If the habit 
in question is such as generally produces conclusions that are sus- 
tained and developed in further inquiry, then it is valid even if in 
an occasional case it yields a conclusion that turns out invalid. In 
such cases, the trouble lies in the material dealt with rather than 
with the habit and general principle. This distinction obviously 
corresponds to the ordinary distinction between form and matter. 
But it does not involve the complete separation between them that 
is often set up in logical theories. 

Any habit is a way or manner of action, not a particular act or 
deed. When it is formulated it becomes, as far as it is accepted, a 
rule, or more generally, a principle or "law" of action. It can 
hardly be denied that there are habits of inference and that they 
may be formulated as rules or principles. If there are such habits 
as are necessary to conduct every successful inferential inquiry, 
then the formulations that express them will be logical principles 
of all inquiries. In this statement "successful" means operative in 
a manner that tends in the long run, or in continuity of inquiry, 
to yield results that are either confirmed in further inquiry or that 
are corrected by use of the same procedures. These guiding 
logical principles are not premises of inference or argument. They 
are conditions to be satisfied such that knowledge of them pro- 
vides a principle of direction and of testing. They are formulations 
of ways of treating subject-matter that have been found to be so 
determinative of sound conclusions in the past that they are taken 
to regulate further inquiry until definite grounds are found for 
questioning them. While they are derived from examination of 
methods previously used in their connection with the kind of con- 



14 INTRODUCTION: THE MATRIX OF IXQUIRY 

elusion they have produced, they are operationally a priori with 
respect to further inquiry. 4 

In the previous discussion I have made statements whose full 
force can become clear only in the more detailed development of 
logical themes in subsequent chapters. The discussion, as was said 
at the outset, is not intended to justify the position but to clarify 
its general meaning. In the remaining pages of this Introduction 
I shall set forth certain implications of the position for the 
theory of logic. 

1. Logic is a progressive discipline. The reason for this is that 
logic rests upon analysis of the best methods of inquiry (being 
judged "best" by their results with respect to continued inquiry) 
that exist at a given time. As the methods of the sciences improve, 
corresponding changes take place in logic. An enormous change 
has taken place in logical theory since the classic logic formulated 
the methods of the science that existed in its period. It has oc- 
curred in consequence of the development of mathematical and 
physical science. If, however, present theory provided a coherent 
formulation of existing scientific methods, freed from a doctrine of 
logical forms inherited from a science that is no longer held, this 
treatise would have no reason for existence. When in the future 
methods of inquiry are further changed, logical theory will also 
change. There is no ground for supposing that logic has been or 
ever will be so perfected that, save, perhaps, for minor details, it 
will require no further modification. The idea that logic is capable 
of final formulation is an eidolon of the theater. 

2. The subject-matter of logic is determined operationally:' 
This thesis is a verbal restatement of what was earlier said. The 
methods of inquiry are operations performed or to be performed. 
Logical forms are the conditions that inquiry, qua inquiry, has 

4 As has been indicated, the above account is a free rendering of Peirce. See 
particularly his Collected Papers, Vol. Ill, pp. 154-68, and Vol. V. pp. 36% 370. 

5 The word "operational" is not a substitute for what is designated by the word 
"instrumental." It expresses the way in and by which the subject-matter of inquiry 
is rendered the means to the end of inquiry, the institution of determinate exist- 
ential situations. As a general term, "instrumental" stands for the relation of 
?neans-consequence i as the basic category for interpretation of logical forms, 
while "operational" stands for the conditions by which subject-matter is (1) 
rendered fit to serve as means and (2) actually functions as such means in effect- 
ing the objective transformation which is the end of inquiry. 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 15 

to meet. Operations, to anticipate, fall into two general types. 
There are operations that are performed upon and with existential 
material — as in experimental observation. There are operations 
performed with and upon symbols. But even in the latter case, 
"operation" is to be taken in as literal a sense as possible. There 
are operations like hunting for a lost coin or measuring land, and 
there are operations like drawing up a balance-sheet. The former 
is performed upon existential conditions; the latter upon symbols. 
But the symbols in the latter case stand for possible final existential 
conditions while the conclusion, when it is stated in symbols, is a 
pre-condition of further operations that deal with existences. 
Moreover, the operations involved in making a balance-sheet for 
a bank or any other business involve physical activities. The so- 
called "mental" element in operations of both these kinds has to be 
defined in terms of existential conditions and consequences, not 
vice-versa. 

Operations involve both material and instrumentalities, including 
in the latter tools and techniques. The more material and in- 
strumentalities are shaped in advance with a view to their operating 
in conjunction with each other as means to consequences, the better 
the operations performed are controlled. Refined steel, which is 
the matter of the operations by which a watch-spring is formed, is 
itself the product of a number of preparatory operations executed 
with reference to getting the material into the state that fits it to be 
the material of the final operation. The material is thus as instru- 
mental, from an operational point of view, as are the tools and 
techniques by which it is brought into a required condition. On 
the other hand, old tools and techniques are modified in order 
that they may apply more effectively to new materials. The intro- 
duction, for example, of the lighter metals demanded different 
methods of treatment from those to which the heavier metals 
previously used were subjected. Or, stated from the other side, 
the development of electrolytic operations made possible the use 
of new materials as means to new consequences. 

The illustration is drawn from the operations of industrial arts. 
But the principle holds of operations of inquiry. The latter also 
proceed by shaping on one hand subject-matter so that it lends 
itself to the application of conceptions as modes of operation; and, 



16 INTRODUCTION: THE MATRIX OF INQUIRY 

on the other hand, by development of such conceptual structures 
as are applicable to existential conditions. Since, as in the arts, 
both movements take place in strict correspondence with each 
other, the conceptions employed are to be understood as directly 
operational, while the existential material, in the degree in which 
the conditions of inquiry are satisfied, is determined both by 
operations and with an eye to operations still to be executed. 

3. Logical forms are postulational. Inquiry in order to be 
inquiry in the complete sense has to satisfy certain demands that 
are capable of formal statement. According to the view that makes 
a basic difference between logic and methodology, the require- 
ments in question subsist prior to and independent (if inquiry. 
Upon that view, they are final in themselves, not intrinsically 
postulational. This conception of them is the ultimate ground of 
the idea that they are completely and inherently a priori and are 
disclosed to a faculty called pure reason. The position here taken 
holds that they are intrinsically postulates of and for inquiry, be- 
ing formulations of conditions, discovered in the course of inquiry 
itself, which further inquiries must satisfy if the}' are to yield 
warranted assertibility as a consequence. 

Stated in terms of the means-consequence relation, they are a 
generalization of the nature of the means that must be employed if 
assertibility is to be attained as an end. Certain demands have to 
be met by the operations that occur in the arts. A bridge is to be 
built to span a river under given conditions, so that the\ridge, as 
the consequence of the operations, will sustain certain loads. 
There are local conditions set by the state of the banks, etc. But 
there are general conditions of distance, weights, stresses and 
strains, changes of temperature, etc. These are formal conditions. 
As such they are demands, requirements, postulates, to be fulfilled. 
^ A postulate is also a stipulation. To engage in an inquiry is 
like entering into a contract. It commits the inquirer to observance 
of certain conditions. A stipulation is a statement of conditions 
that are agreed to in the conduct of some affair. The stipulations 
involved are at first implicit in the undertaking of inquiry. As they 
are formally acknowledged (formulated), they become logical 
forms of various degrees of generality. They make definite what 
is involved in a demand. Every demand is a request, but not every 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 17 

request is a postulate. For a postulate involves the assumption of 
responsibilities. The responsibilities that are assumed are stated in 
stipulations. They involve readiness to act in certain specified 
ways. On this account, postulates are not arbitrarily chosen. 
They present claims to be met in the sense in which a claim 
presents a title or has authority to receive due consideration. 

In engaging in transactions, human beings are not at first aware 
of the responsibilities that are implicit; for laws, in the legal 
sense, are explicit statements of what was previously only implicit 
in customs: namely, formal recognition of duties and rights that 
were practically involved in acceptance of the customs. One of the 
highly generalized demands to be met in inquiry is the following: 
"If anything has a certain property, and whatever has this property 
has a certain other property, then the thing in question has this 
certain other property/' This logical "law" is a stipulation. If 
you are going to inquire in a way which meets the requirements 
of inquiry, you must proceed in a way which observes this rule, 
just as when you make a business contract there are certain con- 
ditions to be fulfilled. 

A postulate is thus neither arbitrary nor externally a priori. It 
is not the former because it issues from the relation of means to the 
end to be reached. It is not the latter, because it is not imposed 
upon inquiry from without, but is an acknowledgement of that to 
which the undertaking of inquiry commits us. It is empirically 
and temporally a priori in the same sense in which the law of 
contracts is a rule regulating in advance the making of certain kinds 
of business engagements. While it is derived from what is involved 
in inquiries that have been successful in the past, it imposes a con- 
dition to be satisfied in future inquiries, until the results of such in- 
quiries show reason for modifying it. 

Terming logical forms postulates is, thus, on the negative side, 
a way of calling attention to the fact that they are not given and 
imposed from without. Just as the postulates of, say, geometry are 
not self-evident first truths that are externally imposed premises 
but are formulations of the conditions that have to be satisfied in 
procedures that deal with a certain subject-matter, so with logical 
forms which hold for every inquiry. In a contract, the agreement 
involved is that between the consequences of the activities of two 



18 



INTRODUCTION: THE MATRIX OF IXQUIRV 



or more parties with respect to some specified affair. In inquiry, 
the agreement is between the consequences of a series of inquiries. 
But inquiry as such is not carried on by one person rather than 
another. When any one person engages in it, he is committed, in 
as far as his inquiry is genuinely such and not an insincere bluff, to 
stand by the results of similar inquiries by whomever conducted. 
"Similar" in this phrase means inquiries that submit to the same 
conditions or postulates. 

The postulational character of logical theory requires, accord- 
ingly, the most complete and explicit formulation that is attainable 
of not only the subject-matter that is taken as evidential in a given 
inference, but also of general conditions, stated in the rules and 
principles of inference and discourse. A distinction of matter and 
form is thus instituted. But it is one in which subject-matter and 
form correspond strictly to each other. Hence, once more, postu- 
lates are not arbitrary or mere linguistic conventions. They must 
be such as control the determination and arrangement of subject- 
matter with respect to achieving cnduringly stable beliefs. Only 
after inquiry has proceeded for a considerable time and has hit 
upon methods that work successfully, is it possible to extract the 
postulates that are involved. They are not presuppositions at 
large. They are abstract in the sense that the}' are derived from 
analytic survey of the relations between methods as means and 
conclusions as consequences — a principle that exemplifies the 
meaning of rationality. 

The postulational nature of logical theory thus agrees with what 
has been said about logic as progressive and operational Postu- 
lates alter as methods of inquiry are perfected; the logical forms 
that express modern scientific inquiry are in many respects quite 
unlike those that formulated the procedures of C J reek science. An 
experimenter in the laboratory who publishes his results states the 
materials used, the setup of apparatus and the procedures employed. 
These specifications are limited postulates, demands and stipula- 
tions, for any inquirer who wishes to test the conclusion reached. 
Generalize this performance for procedures of inquiry as such, 
that is, with respect to the form of every inquiry, and logical 
forms as postulates are the outcome. 

4. Logic is a naturalistic theory. The term "naturalistic" has 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 19 

many meanings. As it is here employed it means, on one side, that 
there is no breach of continuity between operations of inquiry and 
biological operations and physical operations. "Continuity," on 
the other side, means that rational operations grow out of organic 
activities, without being identical with that from which they 
emerge. There is an adjustment of means to consequences in the 
activities of living creatures, even though not directed by deliberate 
purpose. Human beings in the ordinary or "natural" processes of 
living come to make these adjustments purposely, the purpose 
being limited at first to local situations as they arise. In the course 
of time (to repeat a principle already set forth) the intent is so 
generalized that inquiry is freed from limitation to special circum- 
stances. The logic in question is also naturalistic in the sense of the 
observability, in the ordinary sense of the word, of activities of 
inquiry. Conceptions derived from a mystical faculty of intuition 
or anything that is so occult as not to be open to public inspection 
and verification (such as the purely psychical for example) are 
excluded. 

5. Logic is a social discipline. One ambiguity attending the 
word "naturalistic" is that it may be understood to involve reduc- 
tion of human behavior to the behavior of apes, amebae, or 
electrons and protons. But man is naturally a being that lives in 
association with others in communities possessing language, and 
therefore enjoying a transmitted culture. Inquiry is a mode of 
activity that is socially conditioned and that has cultural con- 
sequences. This fact has a narrower and a wider import. Its 
more limited import is expressed in the connection of logic with 
symbols. Those who are concerned with "symbolic logic" do 
not always recognize the need for giving an account of the 
reference and function of symbols. While the relations of symbols 
to one another is important, symbols as such must be finally under- 
stood in terms of the function which symbolization serves. The 
fact that all languages (which include much more than speech) 
consist of symbols, does not of itself settle the nature of symbolism 
as that is used in inquiry. But, upon any naturalistic basis, it 
assuredly forms the point of departure for the logical theory of 
symbols. Any theory of logic has to take some stand on the 
question whether symbols are ready-made clothing for meanings 



20 INTRODUCTION: THE MATRIX OF IXQUIRY^ 

that subsist independently, or whether the}- are necessary con- 
ditions for the existence of meanings— in terms often used, whether 
language is the dress of "thought" or is something without which 
"thought" cannot be. 

The wider import is found in the fact that ever}* inquiry grows 
out of a background of culture and takes effect in greater or less 
modification of the conditions out of which it arises. Merely 
physical contacts with physical surroundings occur. But in every 
interaction that involves intelligent direction, the physical en- 
vironment is part of a more inclusive social or cultural environ- 
ment. Just as logical texts usually remark incidental!}' that reflec- 
tion grows out of the presence of a problem and then proceed as if 
this fact had no further interest for the theory of reflection, so they 
observe that science itself is culturally conditioned and then dis- 
miss the fact from further consideration/"' This wider aspect of the 
matter is connected with what was termed the narrower. 
Language in its widest sense — that is, including all means of com- 
munication such as, for example, monuments, rituals, and formal- 
ized arts — is the medium in which culture exists and through which 
it is transmitted. Phenomena that are not recorded cannot be even 
discussed. Language is the record that perpetuates occurrences 
and renders them amenable to public consideration. On the other 
hand, ideas or meanings that exist ofily in symbols that are not 
communicable are fantastic beyond imagination* The naturalistic 
conception of logic, which underlies the position here taken, is thus 
cultural naturalism. Neither inquiry nor the most abstractly 
formal set of symbols can escape from the cultural matrix in which 
they live, move and have their being. 

6. Logic is autonomous. The position taken implies the 
ultimacy of inquiry in determination of the formal conditions of 
inquiry. Logic as inquiry into inquiry is, if you please, a circular 
process; it does not depend upon anything extraneous to inquiry. 
The force of this proposition may perhaps be most readily under- 
stood by noting what it precludes. It precludes the determination 

G "Not even the physicist is wholly independent of die context of experience 
provided for him by the society within which he works." St ebbing A Modem 
Introduction to Logic, p. 16. If one includes in "society" the community of 
scientific workers, it would seem as if "even" should be changed to read/ "the 
physicist almost more than anyone else." 



THE PROBLEM OF LOGICAL SUBJECT-MATTER 21 

and selection of logical first principles by an a priori intuitional 
act, even when the intuition in question is said to be that of 
Intellects Purus. It precludes resting logic upon metaphysical 
and epistemological assumptions and presuppositions. The latter 
are to be determined, if at all, by means of what is disclosed as the 
outcome of inquiry; they are not to be shoved under inquiry as its 
"foundation." On the epistemological side, it precludes, as was 
noted earlier in another connection, the assumption of a prior 
ready-made definition of knowledge which determines the char- 
acter of inquiry. Knowledge is to be defined in terms of inquiry, 
not vice-versa, both in particular and universally. 

The autonomy of logic also precludes the idea that its "founda- 
tions" are psychological. It is not necessary to reach conclusions 
about sensations, sense-data, ideas and thought, or mental faculties 
generally, as material that preconditions logic. On the contrary, 
just as the specific meaning of these matters is determined in 
specific inquiries, so generally their relation to the logic of inquiry 
is determined by discovering the relation that the subject-matters 
to which these names are given bear to the effective conduct of 
inquiry as such. The point may be illustrated by reference to 
"thought." It would have been possible in the preceding pages 
to use the term "reflective thought" where the word "inquiry" has 
been used. But if that word had been used, it is certain that some 
readers would have supposed that "reflective thought" designated 
something already sufficiently known so that "inquiry" was 
equated to a preexisting definition of thought. The opposite view 
is implied in the position taken. We do not know what meaning 
is to be assigned to "reflective thought" except in terms of what is 
discovered by inquiry into inquiry; at least we do not know what 
it means for the purposes of logic. Personally, I doubt whether 
there exists anything that may be called thought as a strictly 
psychical existence. But it is not necessary to go into that question 
here. For even if there be such a thing, it does not determine the 
meaning of "thought" for logic. 

Either the word "thought" has no business at all in logic or else 
it is a synonym of "inquiry" and its meaning is determined by what 
we find out about inquiry. The latter would seem to be the 
reasonable alternative. These statements do not mean that a 



22 INTRODUCTION: THE MATRIX OF IXQUIRY _ 

sound psychology may not be of decided advantage to logical 
theory. For history demonstrates that unsound psychology has 
done great damage. But its general relation to logic is found in 
the light that it, as a branch of inquiry, may throw upon what is 
involved in inquiry. Its generic relation to logic is similar to that 
of physics or biology. Specifically, for reasons that will appear 
in subsequent chapters, its findings stand closer to logical theory 
than do those of the other sciences. Occasional reference to 
psychological subject-matter is inevitable in any case; lor, as will 
be shown later, some logical positions that pride themselves upon 
their complete indifference to psychological considerations in fact 
rest upon psychological notions that have become so current, so em- 
bedded in intellectual tradition, that they are accepted uncritically 
as if they were self-evident. 

The remaining chapters of Part One are preparatory to the 
later and more detailed outline of what is implied in the proposi- 
tions (1) that logical theory is the systematic formulation of eon- 
trolled inquiry, and (2) that logical forms accrue in and because 
of control that yields conclusions \\ Inch are w arrant ably assemble. 
Were the general point of view even moderately represented in 
current theory these chapters would not be needed. In the present 
state of logical discussion they seem to me to he necessary. Chap- 
ters II and III consider the naturalistic background of the theory, 
one upon its biological side, the other upon the cultural. Chapters 
IV and V endeavor to state the need and importance of a revision 
of logical theory in the direction that has been set forth. 



CHAPTER II 

THE EXISTENTIAL MATRIX OF INQUIRY: 
BIOLOGICAL 



"nJhis chapter and the following one are occupied with de- 
velopment of the statement that logic is naturalistic. The 
present chapter is concerned with the biological natural 
foundations of inquiry. It is obvious without argument that when 
men inquire they employ their eyes and ears, their hands and their 
brains. These organs, sensory, motor or central, are biological. 
Hence, although biological operations and structures are not suf- 
ficient conditions of inquiry, they are necessary conditions. The 
fact that inquiry involves the use of biological factors is usually sup- 
posed to pose a special metaphysical or epistomological problem, 
that of the mind-body relation. When thus shunted off into a 
special domain, its import for logical theory is ignored. When, 
however, biological functions are recognized to be indispensable 
constituents of inquiry, logic does not need to get enmeshed in the 
intricacies of different theories regarding the relations of mind and 
body. It suffices to accept the undeniable fact that they are neces- 
sary factors in inquiry, and then consider how they operate in its 
conduct. The purpose of the following discussion is to show that 
biological functions and structures prepare the way for deliberate 
inquiry and how they foreshadow its pattern. 

The primary postulate of a naturalistic theory of logic is con- 
tinuity of the lower (less complex) and the higher (more complex) 
activities and forms. The idea of continuity is not self-explana- 
tory. But its meaning excludes complete rupture on one side and 
mere repetition of identities on the other; it precludes reduc- 
tion of the "higher" to the "lower" just as it precludes complete 
breaks and gaps. The growth and development of any living 
organism from seed to maturity illustrates the meaning of con- 
tinuity. The method by which development takes place is some- 

23 



24 INTRODUCTION: THE MATRIX OF INQUIRY 

thing to be determined by a study of what actually occurs. It 
is not to be determined by prior conceptual constructions, even 
though such constructions may be helpful as hypotheses when 
they are used to direct observation and experimentation. 

We cannot, for example, say in advance that development pro- 
ceeds by minute increments or by abrupt mutations; that it pro- 
ceeds from the part to the whole by means of compounding of 
elements, or that it proceeds by differentiation of gross wholes into 
definite related parts. None of these possibilities are excluded as 
hypotheses to be tested by the results of investigation. What is 
excluded by the postulate of continuity is the appearance upon 
the scene of a totally new outside force as a cause of changes that 
occur. Perhaps from mutations that are due to some form of 
radio-activity a strikingly new form emerges. But radio-activity 
is not invented ad hoc and introduced from withour in order to 
account for such transformation. It is first known to exist in na- 
ture, and then, if this particular theory of the origin of mutations 
is confirmed, is found actually to occur in biological phenomena 
and to be operative among them in observable and describablc 
fashion. On the other hand, should the conclusion of scientific 
investigation be that development proceeds by minute increments, 
no amount of addition of such increments will constitute develop- 
ment save when their cumulative effect generates something new 
and different. 

The application of the postulate of continuity to discussion of 
logical subject-matter means, therefore, negatively, that in order to 
account for the distinctive, and unique, characters of logical 
subject-matter we shall not suddenly evoke a new power or faculty 
like Reason or Pure Intuition. Positively and concretely, it means 
that a reasonable account shall be given of the ways in which it is 
possible for the traits that differentiate deliberate inquiry to de- 
velop out of biological activities not marked by those traits. It is 
possible, of course, to deal with what was called proximate logical 
subject-matter without raising this question. But it is cause for 
surprise that writers who energetically reject the intervention of 
the supernatural or the non-natural in every other scientific field 
feel no hesitancy in invoking Reason and a priori Intuition in the 
domain of logical theory. It would seem to be more incumbent 



THE EXISTENTIAL MATRIX OF INQUIRY 25 

upon logicians than upon others to make their position in logic 
coherent with their beliefs about other matters. 

If one denies the supernatural, then one has the intellectual re- 
sponsibility of indicating how the logical may be connected with 
the biological in a process of continuous development. This point 
deserves emphasis, for if the following discussion fails to fulfil the 
task of pointing out satisfactorily the continuous path, then that 
failure becomes, for those who accept the naturalistic postulate, 
but a challenge to perform the task better. 

Whatever else organic life is or is not, it is a process of activity 
that involves an environment. It is a transaction extending be- 
yond the spatial limits of the organism. An organism does not live 
in an environment; it lives by means of an environment. Breath- 
ing, the ingestion of food, the ejection of waste products, are cases 
of direct integration; the circulation of the blood and the energiz- 
ing of the nervous system are relatively indirect. But every or- 
ganic function is an interaction of intra-organic and extra-organic 
energies, either directly or indirectly. For life involves expendi- 
ture of energy and the energy expended can be replenished only 
as the activities performed succeed in making return drafts upon 
the environment — the only source of restoration of energy. Not 
even a hibernating animal can live indefinitely upon itself. The 
energy that is drawn is not forced in from without; it is a conse- 
quence of energy expended. If there is a surplus balance, growth 
occurs. If there is a deficit balance, degeneration commences. 
There are things in the world that are indifferent to the life- 
activities of an organism. But they are not parts of its environ- 
ment, save potentially. The processes of living are enacted by the 
environment as truly as by the organism; for they are an integra- 
tion. 

It follows that with every differentiation of structure the en- 
vironment expands. For a new organ provides a new way of in- 
teracting in which things in the world that were previously 
indifferent enter into life-functions. The environment of an ani- 
mal that is locomotor differs from that of a sessile plant; that of a 
jelly fish differs from that of a trout, and the environment of any 
fish differs from that of a bird. So, to repeat what was just said, 
the difference is not just that a fish lives in the water and a bird in 



26 INTRODUCTION: THE MATRIX OF IXQUIRY 

the air, but that the characteristic functions of these animals are 
what they are because of the special way in which water and air 
enter into their respective activities. 

With differentiation of interactions comes the need of maintain- 
ing a balance among them; or, in objective terms, a unified en- 
vironment. The balance has to be maintained by a mechanism 
that responds both to variations that occur within the organism and 
in surroundings. For example, such an apparently self-contained 
function as that of respiration is kept constant by means of active 
exchanges between the alkaline and carbon dioxide contents of 
changing pressures exerted by the blood and the carbon dioxide in 
the lungs. The lungs in turn are dependent upon interactions 
effected by kidneys and liver, which effect the interactions of the 
circulating blood with materials of the digestive tract. This whole 
system of accurately timed interchanges is regulated In* changes in 
the nervous system. 

The effect of this delicate and complex system of internal 
changes is the maintenance of a fairly uniform integration with 
the environment, or — what amounts to the same thing- -a fairly 
unified environment. The interactions of inanimate things with 
their surroundings are not such as to maintain a stable relation 
between the things involved. The blow of a hammer, for example, 
breaks a stone into bits. But as long as life normally continues, 
the interactions to which organic and environmental energies enter 
are such as to maintain the conditions in both of them needed for 
later interactions. The processes, in other words, are self-main- 
taining, in a sense in which they are not in the case of the interac- 
tions of non-living things. 

Capacity for maintenance of a constant form of interaction be- 
tween organism and environment is not confined to the individual 
organism. It is manifested also, in the reproduction of similar or- 
ganisms. The stone is presumably indifferent as to how it reacts 
mechanically and chemically (within the limits of its potentialities) 
to other things. The stone may lose its individuality but basic 
mechanical and chemical processes go on uninterruptedly. As long 
as life continues, its processes are such as continuously "to maintain 
and restore the enduring relationship which is characteristic of the 
life-activities of a given organism. 



THE EXISTENTIAL MATRIX OF INQUIRY 27 

Each particular activity prepares the way for the activity that 
follows. These form not a mere succession but a series. This 
seriated quality of life activities is effected through the delicate 
balance of the complex factors in each particular activity. When 
the balance within a given activity is disturbed — when there is a 
proportionate excess or deficit in some factor — then there is ex- 
hibited need, search and fulfilment (or satisfaction) in the ob- 
jective meaning of those terms. The greater the differentiation of 
structures and their corresponding activities becomes, the more 
difficult it is to keep the balance. Indeed, living may be regarded 
as a continual rhythm of dis equilibrations and recoveries of equi- 
librium. The "higher" the organism, the more serious become 
the disturbances and the more energetic (and often more pro- 
longed) are the efforts necessary for its reestablishment. The state 
of disturbed equilibration constitutes need. The movement to- 
wards its restoration is search and exploration. The recovery is 
fulfilment or satisfaction. 

Hunger, for example, is a manifestation of a state of imbalance 
between organic and environmental factors in that integration 
which is life. This disturbance is a consequence of lack of full 
responsive adaptation to one another of various organic functions. 
The function of digestion fails to meet the demands made upon it 
directly by the circulatory system which carries replenishing nutri- 
tive material to all the organs concerned in the performance of 
other functions, and the demands indirectly made by motor ac- 
tivities. A state of tension is set up which is an actual state (not 
mere feeling) of organic uneasiness and restlessness. This state of 
tension (which defines need) passes into search for material that 
will restore the condition of balance. In the lower organisms it 
is expressed in the bulgings and retractions of parts of the organ- 
ism's periphery so that nutritive material is ingested. The matter 
ingested initiates activities throughout the rest of the animal that 
lead to a restoration of balance, which, as the outcome of the state 
of previous tension, is fulfilment. 

Rignano, in an instructive discussion of the biological basis of 
thinking, says that every organism strives to stay in a stationary 
state. He gives evidence from the activity of lower organisms 
which shows that activities occurring when their state is disturbed 



28 INTRODUCTION: THE MATRIX OF 1NQUIRV 

are such as tend to restore the former stationary condition. 1 He 
also states that "a prior physiological state cannot be perfectly re- 
established and made to persist in normal activity until an animal 
by its movements has succeeded in getting again into an environ- 
ment identical with its old one." His position may be interpreted 
so that what is said in this text is in agreement with it. But as his 
treatment stands, it emphasizes restoration of the previous state of 
the organism rather than the institution of an integrated relation. 
The establishment of the latter relation is compatible with definite 
changes in both the organism and the environment; it does not re- 
quire that old and new states of either the organism or the en- 
vironments be identical with one another. Hence the difference in 
the two views is of considerable theoretical importance. 

If we take as an example the search for food found in connec- 
tion with the higher organisms, it appears clear that the very search 
often leads the organism into an environment that differs from the 
old one, and that the appropriation of food under new conditions 
involves a modified state of the organism. The for?// of the rela- 
tionship, of the interaction, is reinstated, not the identical condi- 
tions. Unless this fact is recognized, development becomes 
abnormal or at least unusual matter rather than a normal feature of 
life activities. Need remains a constant factor but it changes its 
quality. With change in need comes a change in exploratory 
and searching activities; and that change is followed by a changed 
fulfilment or satisfaction. The conservative tendency is doubtless 
strong; there is a tendency to get back. But in at least the more 
complex organisms, the activity of search involves modification of 
the old environment, if only by a change in the connection of the 
organism with it. Ability to make and retain a changed mode of 
adaptation in response to new conditions is the source of that more 
extensive development called organic evolution. Of human or- 
ganisms it is especially true that activities carried on for satisfying 
needs so change the environment that new needs arise which de- 
mand still further change in the activities of the organism by which 
they are satisfied; and so on in a potentially endless chain. 

In the lower organisms, interaction between organic and cn- 

x The Psychology of Reasoning, English translation, p. 6, p. 11 and p. 31. 



THE EXISTENTIAL MATRIX OF INQUIRY 29 

viron-energies takes place for the most part through direct contact. 
The tension in the organism is that between its surface and its in- 
terior. In the organisms that have distance receptors and special 
organs of locomotion, the serial nature of life behavior demands 
that earlier acts in the series be such as to prepare the way for the 
later. The time between the occurrence of need and the occur- 
rence of its satisfaction inevitably becomes longer when the inter- 
action is not one of direct contact. For the attainment of an 
integral relation is then dependent upon establishing connections 
with the things at a distance which arouse exploratory activity 
through stimulation of eye and ear. A definite order of initial, of 
intermediate, and of final or closing activities, is thus instituted. 
The terminus ab quo is fixed by such a condition of imbalance in 
the organism that integration of organic factors cannot be attained 
by any material with which the organism is in direct contact. Cer- 
tain of its activities tend in one direction; others move in a differ- 
ent direction. More particularly, its existing contact-activities and 
those aroused by its distance-receptors, are at odds with each other, 
and the outcome of this tension is that the latter activities domi- 
nate. A satiated animal is not stirred by the sight or smell of the 
prey that moves him when he is hungry. In the hungry creature 
activities of search become a definite intervening or intermediate 
series. At each intermediate stage there is still tension between 
contact activities and those responsive to stimuli through distance- 
receptors. Movement continues until integration is established be- 
tween contact and visual and motor activities, as in the consum- 
matory act of devouring food. 

What has been said describes a difference between modes of 
environing-organical interactions to which the names excitation- 
reaction and stimulus-response may be applied. An animal at rest 
is moved to sniff, say, by a sensory excitation. If this special rela- 
tion is isolated and complete in itself, or is taken to be such, there 
is simply excitation-reaction, as when a person jumps but does 
nothing else when he hears a sudden noise. The excitation is 
specific and so is the reaction. Now suppose an excitation comes 
from a remote object through a distance-receptor, as, the eye. 
There is also excitation-reaction. But if the animal is aroused to 
an act of pursuit the situation is quite different. The particular 



30 INTRODUCTION: THE MATRIX OF INQUIRY 

sensory excitation occurs, but it is coordinated with a larger num- 
ber of other organic processes— those of its digestive and circula- 
tory organs and its neuro-muscular system, autonomic, proprio- 
ceptor and central. This coordination, which is a state of the total 
organism, constitutes a stimulus. The difference between this con- 
dition (whatever name it be called by) and a specific sensory 
excitation, is enormous. The pursuit of prey is a response to the 
total state of the organism, not to a particular sensory excitation. 
Indeed, the distinction between what has been called stimulus and 
response is made only by analytic reflection. The so-called stimu- 
lus, being the total state of the organism, moves of itself, because 
of the tensions contained, into those activities of pursuit which are 
called the response. The stimulus is simply the earlier part of the 
total coordinated serial behavior and the response the later part. 

The principle involved in the distinction just drawn is more im- 
portant than it may seem to be at first sight. If it is ignored, the 
sequential character of behavior is lost from view. Behavior then 
becomes simply a succession of isolated and independent units of 
excitation-reaction, which would be comparable, say, to a succes- 
sion of muscular twitches due to a disordered nervous mechanism. 
When the stimulus is recognized to be the tension in the total 
organic activity (ultimately reducible to that between contact 
activities and those occasioned through distance-receptors), it is 
seen that the stimulus in its relationship to special activities persists 
throughout the entire pursuit, although it changes its actual content 
at each stage of the chase. As the animal runs, specific sensory 
excitations, those of contact and those that are olfactory and visual, 
alter with every change of position; with every change in the char- 
acter of the ground; with changing objects (like bushes and rocks) 
that progressively intervene; and they also change in intensity with 
every change in distance from the hunted object. 

The changing excitations are, however, integrated into a single 
stimulus by the total state of the organism. The theory that 
identifies stimuli with a succession of specific sensory excitations, 
cannot possibly account for such unified and continuous responses 
as hunting and stalking prey. On that theory the animal would 
have to make at each stage a new and isolated "response" (reac- 
tion) to everything that came across his path. He would be re- 



THE EXISTENTIAL MATRIX OF INQUIRY 31 

acting to stones, bushes and to changes in the levels and character 
of the ground in so many independent acts that there would be 
no continuity of behavior. He would forget, as we say, what he 
was after in the multitude of separate reactions he would have to 
make to independent excitations. Because behavior is in fact a 
function of the total state of the organism in relation to environ- 
ment, stimuli are functionally constant in spite of changes in 
specific content. Because of this fact, behavior is sequential, one 
act growing out of another and leading cumulatively to a further 
act until the consummatory fully integrated activity occurs. 

Because organic behavior is what it is, and not a succession and 
compounding of independent discrete reflex-arc units, it has direc- 
tion and cumulative force. There are special acts, like winking or 
the knee-jerk, that exemplify the isolated reflex-arc that is some- 
times supposed to be the unit which, through compounding, con- 
stitutes behavior. But there is no evidence that such acts have 
played any role in development. On the contrary, the available 
evidence shows that they are end-points of highly specialized lines 
of development, or else are coincident by-products of the behavior 
of structures that have arisen developmentally. 

What exists in normal behavior-development is thus a circuit of 
which the earlier or "open" phase is the tension of various ele- 
ments of organic energy, while the final and "closed" phase is the 
institution of integrated interaction of organism and environment. 
This integration is represented upon the organic side by equilibra- 
tion of organic energies, and upon the environmental side by the 
existence of satisfying conditions. In the behavior of higher or- 
ganisms, the close of the circuit is not identical with the state out of 
which disequilibration and tension emerged. A certain modifica- 
tion of environment has also occurred, though it may be only a 
change in the conditions which future behavior must meet. On 
the other hand, there is change in the organic structures that con- 
ditions further behavior. This modification constitutes what is 
termed habit. 

Habits are the basis of organic learning. According to the 
theory of independent successive units of excitation-reaction, habit- 
formation can mean only the increasing fixation of certain ways 



32 INTRODUCTION: THE MATRIX OF INQUIRY 

of behavior through repetition, and an attendant weakening of 
other behavioral activities. 2 

Developmental behavior shows, on the other hand, that in the 
higher organisms excitations are so diffusely linked with reactions 
that the sequel is affected by the state of the organism in relation 
to environment. In habit and learning the linkage is tightened up 
not by sheer repetition but by the institution of effective integrated 
interaction of organic-environing energies — the consummatory 
close of activities of exploration and search. In organisms of the 
higher order, the special and more definite pattern of recurrent 
behavior thus formed does not become completely rigid. It enters 
as a factorial agency, along with other patterns, in a total adaptive 
response, and hence retains a certain amount of flexible capacity 
to undergo further modifications as the organism meets new en- 
vironing conditions. 

There is, for example, reciprocal excitation between hand and 
eye activity; a movement of the hand is aroused by visual activity, 
then the movement of the hand is followed by a change in visual 
activity, and so on. Here is a definite recurring pattern of action. 
If the hand never did but one thing, say reach, then this habit- 
pattern might become rigidly set. But the hand also grabs, pushes, 
draws and manipulates. Visual behavior has to be responsive to 
the performance of a great variety of manual activities. It thus 
maintains flexibility and readaptability; the connection between 
hand and eye does not become a rigid bond. 

The view that habits are formed by sheer repetition puts the 
cart before the horse. Ability to repeat is a result of a formation 
of a habit through the organic redispositions effected by attainment 
of a consummatory close. This modification is equivalent to giv- 
ing some definite direction of future actions. As far as environing 
conditions remain much the same, the resulting act will look like 
a repetition of a previously performed act. But even then repeti- 
tion will not be exact as far as conditions differ. Sheer repetition 

2 The effect of terminal success or consummatory satisfaction in determining 
habit has always been a stumbling-block to those who hold that there are ele- 
mentary excitation-reaction "bonds." But this effect is just what should he 
expected on the ground of the view expounded in the text, since it is an expres- 
sion of the fact that the stimulus-response relation is a function of the state of the 
organism as a whole. 



THE EXISTENTIAL MATRIX OF INQUIRY 33 

is, in the case of the human organism, the product of conditions 
that are uniform because they have been made so mechanically — 
as in much school and factory "work." Such habits are limited 
in their manifestation to the rather artificial conditions in which 
they operate. They certainly do not provide the model upon 
which a theory of habit formation and operation should be framed. 

From the foregoing considerations certain general conclusions 
follow as to the nature of the pattern of inquiry as a development 
out of certain aspects of the pattern of life-activities. 3 

1. Environmental conditions and energies are inherent in inquiry 
as a special mode of organic behavior. Any account of inquiry 
that supposes the factors involved in it, say, doubt, belief, observed 
qualities and ideas, to be referable to an isolated organism (subject, 
self, mind) is bound to destroy all ties between inquiry as reflective 
thought and as scientific method. Such isolation logically entails 
a view of inquiry which renders absurd the idea that there is a 
necessary connection between inquiry and logical theory. But the 
absurdity rests upon the acceptance of an unexamined premise 
which is the product of a local "subjectivistic" phase of European 
philosophy. If what is designated by such terms as doubt, belief, 
idea, conception, is to have any objective meaning, to say nothing 
of public verifiability, it must be located and described as behavior 
in which organism and environment act together, or inter-act. 

The earlier discussion set out with the familiar common sense 
distinction of organism and environment, and went on to speak of 
their interaction. Unfortunately, however, a special philosophical 
interpretation may be unconsciously read into the common sense 
distinction. It will then be supposed that organism and environ- 
ment are "given" as independent things and interaction is a third 
independent thing which finally intervenes. In fact, the distinc- 
tion is a practical and temporal one, arising out of the state of 
tension in which the organism at a given time, in a given phase of 
life-activity, is set over against the environment as it then and there 
exists. There is, of course, a natural world that exists independ- 
ently of the organism, but this world is environment only as it 
enters directly and indirectly into life-functions. The organism is 

3 The more specific points of connection are taken up in Ch. VI. 



34 INTRODUCTION: THE MATRIX OF INQUIRY 

itself a part of the larger natural world and exists as organism only 
in active connections with its environment. 

Integration is more fundamental than is the distinction designated 
by interaction of organism and environment. The latter is indica- 
tive of a partial disintegration of a prior integration, but one which 
is of such a dynamic nature that it moves (as long as life continues) 
toward redintegration. 

2. The structure and course of life-behavior has a definite pat- 
tern, spatial and temporal. This pattern definitely foreshadows 
the general pattern of inquiry. For inquiry grows out of an earlier 
state of settled adjustment, which, because of disturbance, is inde- 
terminate or problematic (corresponding to the first phase of 
tensional activity), and then passes into inquiry proper, (corre- 
sponding to the searching and exploring activities of an organism) ; 
when the search is successful, belief or assertion is the counterpart, 
upon this level, of redintegration upon the organic level. 

A detailed account of the pattern of inquiry is given in Chapter 
VI. But the following considerations flow so directly from the 
pattern of life-behavior that they should be noted here: 

a. There is no inquiry that does not involve the making of some 
change in environing conditions. This fact is exemplified in the 
indispensable place of experiment in inquiry, since experimentation 
is deliberate modification of prior conditions. Kvcn in the p re- 
scientific stage, an individual moves head, eyes, often the entire 
body, in order to determine the conditions to be taken account of 
in forming a judgment; such movements effect a change in en- 
vironmental relations. Active pressure by touch, the acts of push- 
ing, pulling, pounding and manipulating to find out what things 
"are like" is an even more overt approach to scientific experimenta- 
tion. 

b. The pattern is serial or sequential. It has already been noted 
that this trait of life-behavior becomes more marked with the 
emergence of distance-receptors and of the neural apparatus neces- 
sary for coordinating their excitation with contact-receptors and 
with the muscular, circulatory and respiratory mechanisms which 
are involved in behavior. In the human organism, organic reten- 
tion (or habit-patterns) give rise to recollection. Goals or conse- 
quences that are even more remote in time and space are then set 



THE EXISTENTIAL MATRIX OF INQUIRY 35 

up and the intervening process of search becomes more seriated 
in temporal span and in connecting links than in the case of the 
simple presence of distance-stimuli. Formation of an end-in-view, 
or consequence to be brought about, is conditioned by recollec- 
tion; it requires making plans in conjunction with selection and 
ordering of the consecutive means by which the plan may become 
an actuality. 

c. The serially connected processes and operations by means of 
which a consummatory close is brought into being are, by descrip- 
tion, intermediate and instrumental. This distinctive characteristic 
prefigures, on the biological level, the interpretation that must be 
given, upon the level of inquiry, to operations of inference and 
discourse in their relation to final judgment as the consummation 
of inquiry. 

d. The basic importance of the serial relation in logic is rooted 
in the conditions of life itself. Modification of both organic and 
environmental energies is involved in life-activity. This organic 
fact foreshadows learning and discovery, with the consequent out- 
growth of new needs and new problematic situations. Inquiry, in 
settling the disturbed relation of organism-environment (which 
defines doubt) does not merely remove doubt by recurrence to a 
prior adaptive integration. It institutes new environing conditions 
that occasion new problems. What the organism learns during 
this process produces new powers that make new demands upon 
the environment. In short, as special problems are resolved, new 
ones tend to emerge. There is no such thing as a final settlement, 
because every settlement introduces the conditions of some degree 
of a new unsettling. In the stage of development marked by the 
emergence of science, deliberate institution of problems becomes 
an objective of inquiry. Philosophy, in case it has not lost touch 
with science, may play an important role in determining formula- 
tion of these problems and in suggesting hypothetical solutions. 
But the moment philosophy supposes it can find a final and com- 
prehensive solution, it ceases to be inquiry and becomes either 
apologetics or propaganda. 

e. From the postulate of naturalistic continuity, with its prime 
corollary that inquiry is a development out of organic-environ- 
mental integration and interaction, something follows regarding 



36 INTRODUCTION: THE MATRIX OF INQUIRY 

the relation of psychology and logic. The negative side of this 
conclusion has already been suggested. The assumptions of ik tnen- 
talistic" psychology have no place in logical theory. The divorce 
between logic and scientific methodology, discussed in the previous 
chapter, has its basis largely in the belief that since inquiry involves 
doubt, suggestion, observation, conjecture, sagacious discernment, 
etc., and since it is assumed that all these things are "mentalistic," 
there is a gulf between inquiry (or reflective thinking) and lo^ic. 
Given the assumption, the conclusion is just. But the recognition 
of the natural continuity of inquiry with organic behavior — the fact 
that it is a developed mode of such behavior — destroys the assump- 
tion. The student of intellectual history is aware of how the new 
scientific standpoint of the sixteenth and seventeenth centuries 
succeeded in setting up a gulf between the mcnral and the physical. 
The former was supposed to constitute a domain of existence of 
psychical "stuff" marked by processes totally unlike those of the 
external world which confronted "mind." The older Greek con- 
ception that the difference was one in the type of organization of 
common materials and processes, was lost from view. Psychology 
and epistemology accepted complete dualism, the "bifurcation" 
of nature, and the theory of thought and ideas was wrought into 
conformity with the dualistic assumption. 

On the positive side, psychology is itself a special branch of in- 
quiry. In general, it bears the same relation to the theory of logical 
inquiry that is sustained by physics or chemistry. Bur as It is 
more directly concerned with the focal center of initiation and 
execution of inquiry than are these other sciences, it may, if em- 
ployed as servant and not as master of logic, make a contribution 
to logical theory which they cannot make". Personally, as has just 
been said, I doubt the existence of anything "mental" in the doc- 
trinal sense alleged. But it is not necessary to go into that question, 
for, as was stated, if there is anything of this kind it is irrelevant to 
.the theory of inquiry. Moreover, any investigation into it must 
itself be an inquiry that satisfies the logical conditions of all inquiry. 
Nevertheless, whatever throws any light upon the organic condi- 
tions and processes that are involved in the occurrence and conduct 
of inquiry (as a sound biological psychology cannot fail to do) can 



THE EXISTENTIAL MATRIX OF INQUIRY 37 

hardly fail to make valuable contributions to the results of inquiry 
into inquiry. 

The points that have been made may be gathered together by 
consideration of the current meaning of "experience," especially 
in connection with the intensified ambiguity, due to historical 
changes, that is attached to "empirical." Experience has a favor- 
able or honorific use, as when it is said that a certain conclusion or 
theory is experientially verified, and is thereby marked off from a 
wild fancy, a happy guess and from a merely theoretical construc- 
tion. On the other hand, because of the influence of psychological 
epistemology of a subjective, private type, "experience" has been 
limited to conscious states and processes. The contrast of the two 
meanings is radical. When it is said that certain conclusions are 
experientially or empirically confirmed, a scientist means anything 
but that they rest upon mental and personal states of mind. Again, 
the word "empirical" is often set in opposition to the rational, and 
this opposition adds to the confusion. The early meaning of "em- 
pirical" limited the application of the word to conclusions that 
rest upon an accumulation of past experiences to exclusion of in- 
sight into principles. 

Thus a medical practitioner may have skill in recognizing the 
symptoms of disease and skill in their treatment because of re- 
peated past observations and customary modes of treatment, with- 
out understanding the etiology of disease and the reasons for the 
kind of treatment employed. The same thing holds of the skills 
of many mechanics and artisans. "Empirical" in this sense de- 
scribes an actual fact and is justly distinguished from "rational" 
activity, meaning, by that word, conduct grounded in understand- 
ing of principles. But it is evident that when a scientific conclusion 
is said to be empirically established, no such exclusion of rationality 
or reasoning is intended or involved. On the contrary, every 
conclusion scientifically reached as to matters of fact involves rea- 
soning with and from principles, usually mathematically expressed. 
To say, then, that it is empirically established is to say the op- 
posite of what is said when "empirical" means only observations and 
habitual response to what is observed. The conversion of a justi- 
fiable distinction between empirical as defined in terms of the 
knowledge and action of artisans and rational as defined in terms 



38 INTRODUCTION: THE MATRIX OF INQUIRY 

of scientific understanding, into something absolute which sets 
every mode of experience in opposition to reason and the rational, 
depends accordingly, upon an arbitrary preconception as to what 
experience and its limits must be. Unfortunately, this arbitrary 
limitation still operates, as in many interpretations of the distinction 
between, say, temporal and eternal objects, perception and concep- 
tion, and, more generally, matter and form. 

It may be added that the honorific use of "experience" when it 
first appeared was undoubtedly overweighted upon the side of 
observation, as in the case of Bacon and Locke. This overweight 
is readily accounted for as a historic occurrence. For the classic 
tradition had degenerated into a form in which it was supposed that 
beliefs about matters of fact could and should be reached by rea- 
soning alone; save as they were established by authority. Opposi- 
tion to this extreme view evoked an equally one-sided notion that 
mere sense-perception could satisfactorily determine beliefs about 
matters of fact. It led in Bacon, as later in Mill, to a neglect of 
the role of mathematics in scientific inquiry, and in Locke to a 
pretty sharp division between knowledge of matters of fact and 
of relations between ideas. The latter, moreover, rested finally 
according to him upon sheer observation, "internal" or "external." 
The final outcome was a doctrine that reduced "experience" to 
"sensations" as the constituents of all observation, and "thought" 
to external associations among these elements, both sensations and 
associations being supposed to be merely mental or psychical. 

The problem of the relation between material that is observed 
and subject-matter that is conceived or thought of is a real one, 
especially in respect to its logical equivalents. But the solution of 
the problem should not be compromised at the outset by a state- 
ment of it in terms of a fixed and absolute distinction between the 
experiential and the rational. Such a statement implies that there 
is no logical problem, but a separation absolutely and immediately 
given. Justification cannot be given at this stage of the discussion 
for the belief that, in a proper conception of experience, inference, 
reasoning and conceptual structures are as experiential as is observa- 
tion, and that the fixed separation between the former and the 
latter has no warrant beyond an episode in the history of culture. 
Upon the basis of the naturalistic position here taken, there is a 



THE EXISTENTIAL MATRIX OF INQUIRY 39 

problem, which takes the following form: How does it come 
about that the development of organic behavior into controlled 
inquiry brings about the differentiation and cooperation of ob- 
servational and conceptual operations? 

The discussion of language and linguistic symbols in the follow- 
ing chapter lays the basis for an answer. But it must be repeated 
that adherence to a tradition that was formed before modern 
scientific inquiry (including the biological) had arisen or been 
subjected to independent analysis, should not be permitted to con- 
vert a problem that holds for all schools alike, into an alleged 
ready-made solution. For such a solution prevents the problem 
from being seen as a problem. Finally, while the position here 
taken implies that logic is empirical in that its subject-matter con- 
sists of inquiries that are publicly accessible and open to observa- 
tion, it is not empirical in the sense in which Mill, for example, 
developed the ideas of Locke and Hume. It is experiential in the 
same way in which the subject-matter and conclusions of any nat- 
ural science are empirical: experiential in the way any natural 
science is experiential, that is, as distinct from the merely specula- 
tive and from the a priori and intuitional. 

I close with a reference to a predicament in which both organic 
behavior and deliberate inquiry are caught. There always exists a 
discrepancy between means that are employed and consequences 
that ensue; sometimes this discrepancy is so serious that its re- 
sult is what we call mistake and error. The discrepancy exists 
because the means used, the organs and habits of biological be- 
havior and the organs and conceptions employed in deliberate 
inquiry, must be present and actual, while consequences to be at- 
tained are future. Present actual means are the result of past con- 
ditions and past activities. They operate successfully, or "rightly," 
in ( 1 ) the degree in which existing environing conditions are very 
similar to those which contributed in the past to formation of the 
habits, and (2) in the degree in which habits retain enough flexibil- 
ity to readapt themselves easily to new conditions. The latter 
condition is not readily fulfilled by lower organisms; when it is 
fulfilled a case of "evolution" occurs. The potential conditions 
for its fulfilment are present in the activities of human beings in 
much larger measure. But the inertial phase of habit is strong, and, 



40 INTRODUCTION: THE MATRIX OF INQUIRY 

so far as it is yielded to, human beings continue to live upon a 
relatively animal plane. Even the history of science has been 
marked by epochs in which observation and reflection have oper- 
ated only within a predetermined conceptual framework — an ex- 
ample of the inertia-phase of habit. That the only way to avoid 
and avert the mistakes of this fixation is by recognition of the 
provisional and conditional nature (as respects any inquiry in 
process) of the facts that enter into it, and the hypothetical nature 
of the conceptions and theories employed, is a relatively late dis- 
covery. The meaning of the discovery has hardly penetrated yet 
into inquiry about the subjects of the greatest practical importance 
to man, religion, politics and morals. 

The recognition of what Peirce called "fallibilism" in distinction 
from "infallibilism" is something more than a prudential maxim. 
It results of necessity from the possibility and probability of a dis- 
crepancy between means available for use and consequences that 
follow; between past and future conditions, not from mere weak- 
ness of mortal powers. Because we live in a world in process, the 
future, although continuous with the past, is not its bare repetition. 
The principle applies with peculiar force to inquiry about inquiry, 
including, needless to say, the inquiry presented in this treatise. 
The very words which must be used are words that have had their 
meanings fixed in the past to express ideas that arc unlike those 
which they must now convey if they are to express what is in- 
tended. To those who are naturalistically inclined, the attendant 
"fallibility" will be but a spur to do better the work which this 
volume attempts to do. The present volume is an approach not 
a closed treatise. The aim it hopes to fulfil is that of being a 
sufficiently coherent and systematic approach to move others to 
undertake the long cooperative work (never-ending in any case as 
long as inquiry continues) needed to test and fill inthe framework 
which is outlined in this book. 

The important matter is that those who reject the doctrine of the 
intervention of some supernatural agency should not be led, by the 
fact that it is not customary to introduce biological considerations 
into the discussion of logical theory, to dismiss the chapter as ir- 
relevant. Those who believe in such intervention have ground 
for belief in an a priori Reason upon which logical f onus and prin- 



THE EXISTENTIAL MATRIX OF INQUIRY 41 

ciples depend; they are precommitted to belief in the irrelevancy of 
all considerations of the order of those here presented. But any 
thoroughgoing naturalist is equally committed by the logic of his 
position to belief in continuity of development, with its corrollary 
of community of factors in the respective patterns of logical and 
biological forms and procedures. 



CHAPTER III 

THE EXISTENTIAL MATRIX OF INQUIRY 
CULTURAL 

^he environment in which human beings live, act and in- 
quire, is not simply physical. It is cultural as well. Prob- 
lems which induce inquiry grow out of the relations of 
fellow beings to one another, and the organs for dealing with 
these relations are not only the eye and ear, but the meanings 
which have developed in the course of living, together with the 
ways of forming and transmitting culture with all its constituents 
of tools, arts, institutions, traditions and customary beliefs. 

I. To a very large extent the ways in which human beings re- 
spond even to physical conditions are influenced by their cultural 
environment. Light and fire are physical facts. But the occasions 
in which a human being responds to things as merely physical in 
purely physical ways are comparatively rare. Such occasions arc 
the act of jumping when a sudden noise is heard, withdrawing the 
hand when something hot is touched, blinking in the presence of 
a sudden increase of light, animal-like basking in sunshine, etc. 
Such reactions are on the biological plane. But the typical cases 
of human behavior are not represented by such examples. The 
use of sound in speech and listening to speech, making and en- 
joying music; the kindling and tending of fire to cook and to keep 
warm; the production of light to carry on and regulate occupa- 
tions and social enjoyments: — these things are representative of 
distinctively human activity. 

To indicate the full scope of cultural determination of the con- 
duct of living one would have to follow the behavior of an in- 
dividual throughout at least a day; whether that of a day laborer, 
of a professional man, artist or scientist, and whether the individual 
be a growing child or a parent. For the result would show how 
thoroughly saturated behavior is with conditions and factors that 

42 



THE EXISTENTIAL MATRIX OF INQUIRY 43 

are of cultural origin and import. Of distinctively human be- 
havior it may be said that the strictly physical environment is so 
incorporated in a cultural environment that our interactions with 
the former, the problems that arise with reference to it, and our 
ways of dealing with these problems, are profoundly affected by 
incorporation of the physical environment in the cultural. 

Man, as Aristotle remarked, is a social animal. This fact intro- 
duces him into situations and originates problems and ways of 
solving them that have no precedent upon the organic biological 
level. For man is social in another sense than the bee and ant, 
since his activities are encompassed in an environment that is cul- 
turally transmitted, so that what man does and how he acts, is de- 
termined not by organic structure and physical heredity alone but 
by the influence of cultural heredity, embedded in traditions, in- 
stitutions, customs and the purposes and beliefs they both carry 
and inspire. Even the neuro-muscular structures of individuals 
are modified through the influence of the cultural environment 
upon the activities performed. The acquisition and understanding 
of language with proficiency in the arts (that are foreign to other 
animals than men) represent an incorporation within the physical 
structure of human beings of the effects of cultural conditions, an 
interpenetration so profound that resulting activities are as direct 
and seemingly "natural" as are the first reactions of an infant. To 
speak, to read, to exercise any art, industrial, fine or political, are 
instances of modifications wrought within the biological organism 
by the cultural environment. 

This modification of organic behavior in and by the cultural en- 
vironment accounts for, or rather is, the transformation of purely 
organic behavior into behavior marked by intellectual properties 
with which the present discussion is concerned. Intellectual opera- 
tions are foreshadowed in behavior of the biological kind, and the 
latter prepares the way for the former. But to foreshadow is not 
to exemplify and to prepare is not to fulfil. Any theory that 
rests upon a naturalistic postulate must face the problem of the 
extraordinary differences that mark off the activities and achieve- 
ments of human beings from those of other biological forms. It 
is these differences that have led to the idea that man is completely 
separated from other animals by properties that come from a non- 



44 INTRODUCTION: THE MATRIX OF INQUIRY __ 

natural source. The conception to be developed in the present 
chapter is that the development of language (in its widest sense) 
out of prior biological activities is, in its connection with wider cul- 
tural forces, the key to this transformation. The problem, so 
viewed, is not the problem of the transition of organic behavior 
into something wholly discontinuous with it— as is the case when, 
for example, Reason, Intuition and the A priori are appealed to for 
explanation of the difference. It is a special form of the general 
problem of continuity of change and the emergence of new modes 
of activity — the problem of development at any level. 

Viewing the problem from this angle, its constituents may be 
reduced to certain heads, three of which will be noted. Organic 
behavior is centered in particular organisms. This statement 
applies to inferring and reasoning as existential activities. But if in- 
ferences made and conclusions reached are to be valid, the subject- 
matter dealt with and the operations employed must be such as to 
yield identical results for all who infer and reason. If the same 
evidence leads different persons to different conclusions, then either 
the evidence is only speciously the same, or one conclusion (or 
both) is wrong. The special constitution of an individual organ- 
ism which plays such a role in biological behavior is so irrelevant 
in controlled inquiry that it has to be discounted and mastered. 

Another phase of the problem is brought out bv the part played 
in human judgments by emotion and desire. These personal traits 
cook the evidence and determine the result that is reached. That 
is, upon the level of organic factors (which are the actively 
determining forces in the type of cases just mentioned), the in- 
dividual with his individual peculiarities, whether native or ac- 
quired, is an active participant in producing ideas and beliefs, and 
yet the latter are logically grounded only when such peculiarities 
are deliberately precluded from taking effect. This point restates 
what was said in connection with the first point, but it indicates 
another phase of the matter. If, using accepted terminology, wc 
say that the first difference is that between the singular and the 
general, the present point may be formulated as the difference be- 
tween the subjective and the objective. To be intellectually "ob- 
jective" is to discount and eliminate merely personal factors in the 
operations by which a conclusion is reached. 



THE EXISTENTIAL MATRIX OF INQUIRY 45 

Organic behavior is a strictly temporal affair. But when be- 
havior is intellectually formulated, in respect both to general ways 
of behavior and the special environing conditions in which they 
operate, propositions result and the terms of a proposition do not 
sustain a temporal relation to one another. It was a temporal 
event when someone landed on Robinson Crusoe's island. It was 
a temporal event when Crusoe found the footprint on the sands. 
It was a temporal event when Crusoe inferred the presence of a 
possibly dangerous stranger. But while the proposition was about 
something temporal, the relation of the observed fact as evidential 
to the inference drawn from it is non-temporal. The same holds 
of every logical relation in and of propositions. 

In the following discussion it is maintained that the solution of 
the problem just stated in some of its phases, is intimately and 
directly connected with cultural subject-matter. Transformation 
from organic behavior to intellectual behavior, marked by logical 
properties, is a product of the fact that individuals live in a cultural 
environment. Such living compels them to assume in their be- 
havior the standpoint of customs, beliefs, institutions, meanings and 
beliefs which are at least relatively general and objective. 1 

II. Language occupies a peculiarly significant place and exercises 
a peculiarly significant function in the complex that forms the cul- 
tural environment. It is itself a cultural institution, and, from one 
point of view, is but one among many such institutions. But it is 
( 1 ) the agency by which other institutions and acquired habits are 
transmitted, and (2) it permeates both the forms and the contents 
of all other cultural activities. Moreover, (3) it has its own dis- 
tinctive structure which is capable of abstraction as a form. This 
structure, when abstracted as a form, had a decisive influence his- 
torically upon the formulation of logical theory; the symbols which 
are appropriate to the form of language as an agency of inquiry 
(as distinct from its original function as a medium of communica- 
tion) are still peculiarly relevant to logical theory. Consequently, 
further discussion will take the wider cultural environment for 
granted and confine itself to the especial function of language in 
effecting the transformation of the biological into the intellectual 
and the potentially logical. 

1 The non-temporal phase of propositions receives attention later. 



46 INTRODUCTION: THE MATRIX OF INQUIRY^ 

In this further discussion, language is taken in its widest sense, a 
sense wider than oral and written speech. It includes the latter. 
But it includes also not only gestures but rites, ceremonies, monu- 
ments and the products of industrial and fine arts. A tool or ma- 
chine, for example, is not simply a simple or complex physical 
object having its own physical properties and effects, but is also a 
mode of language. For it says something, to those who understand 
it, about operations of use and their consequences. To the mem- 
bers of a primitive community a loom operated by steam or elec- 
tricity says nothing. It is composed in a foreign language, and so 
with most of the mechanical devices of modern civilization. In the 
present cultural setting, these objects are so intimately hound up 
with interests, occupations and purposes that they have an eloquent 
voice. 

The importance of language as the necessary, and, in the end, 
sufficient condition of the existence and transmission of non-purely 
organic activities and their consequences lies in the fact that, on 
one side, it is a strictly biological mode of behavior, emerging in 
natural continuity from earlier organic activities, while, on the 
other hand, it compels one individual to take the standpoint of 
other individuals and to see and inquire from a standpoint that is 
not strictly personal but is common to them as participants or 
"parties" in a conjoint undertaking. It ma}' be directed bv and to- 
wards some physical existence. But it first has reference to some 
other person or persons with whom it institutes communication — 
the making of something common. 1 Icnec, to that extent its refer- 
ence becomes general and "objective." 

Language is made up of physical existences; sounds, or marks 
on paper, or a temple, statue, or loom. But these do not operate 
or function as mere physical things when they are media of com- 
munication. They operate in virtue of their representative ca- 
pacity or meaning. The particular physical existence which has 
meaning is, in the case of speech, a conventional matter. But the 
convention or common consent which sets it apart as a means of 
recording and communicating meaning is that of agreement in 
action; of shared modes of responsive behavior and participation 
in their consequences. The physical sound or mark gets its mean- 
ing in and by conjoint community of functional use, not by any 



THE EXISTENTIAL MATRIX OF INQUIRY 47 

explicit convening in a "convention" or by passing resolutions that 
a certain sound or mark shall have a specified meaning. Even 
when the meaning of certain legal words is determined by a court, 
it is not the agreement of the judges which is finally decisive. 
For such assent does not finish the matter. It occurs for the sake 
of determining future agreements in associated behavior, and it is 
this subsequent behavior which finally settles the actual meaning 
of the words in question. Agreement in the proposition arrived 
at is significant only through this function in promoting agreement 
in action. 

The reason for mentioning these considerations is that they 
prove that the meaning which a conventional symbol has is not 
itself conventional. For the meaning is established by agreements 
of different persons in existential activities having reference to 
existential consequences. The particular existential sound or mark 
that stands for dog or justice in different cultures is arbitrary or 
conventional in the sense that although it has causes there are no 
reasons for it. But in so far as it is a medium of communication, 
its meaning is common, because it is constituted by existential con- 
ditions. If a word varies in meaning in intercommunication be- 
tween different cultural groups, then to that degree communica- 
tion is blocked and misunderstanding results. Indeed, there ceases 
to be communication until variations of understanding can be 
translated, through the meaning of words, into a meaning that is 
the same to both parties. Whenever communication is blocked 
and yet is supposed to exist misunderstanding, not merely absence 
of understanding, is the result. It is an error to suppose that the 
misunderstanding is about the meaning of the 'word in isolation, 
just as it is fallacious to suppose that because two persons accept 
the same dictionary meaning of a word they have therefore come 
to agreement and understanding. For agreement and disagree- 
ment are determined by the consequences of conjoint activities. 
Harmony or the opposite exists in the effects produced by the 
several activities that are occasioned by the words used. 

III. Reference to concord of consequences as the determinant 
of the meaning of any sound used as a medium of communication 
shows that there is no such thing as a mere word or mere symbol. 
The physical existence that is the vehicle of meaning may as a 



48 INTRODUCTION: THE MATRIX OF INQUIRY ^ 

particular be called mere; the recitation of a number of such 
sounds or the stringing together of such marks may be called mere 
language. But in fact there is no word in the first case and no 
language in the second. The activities that occur and the conse- 
quences that result which are not determined by meaning, are, 
by description, only physical. A sound or mark of any physical 
existence is a part of language only in virtue of its operational 
force; that is, as it functions as a means of evoking different activi- 
ties performed by different persons so as to produce consequences 
that are shared by all the participants in the conjoint undertaking. 
This fact is evident and direct in oral communication. It is in- 
direct and disguised in written communication. Where written 
literature and literacy abound, the conception of language is likely 
to be framed upon their model. The intrinsic connection of lan- 
guage with community of action is then forgotten. Language is 
then supposed to be simply a means of expressing or communicat- 
ing "thoughts" — a means of conveying ideas or meanings that are 
complete in themselves apart from communal operational force. 

Much literature is read, moreover, simply for enjoyment, for 
esthetic purposes. In this case, language is a means of action only 
as it leads the reader to build up pictures and scenes to be enjoyed 
by himself. There ceases to be immediate inherent reference to 
conjoint activity and to consequences mutually participated in. 
Such is not the case, however, in reading to get at the meaning of 
the author; that is, in reading that is emphatically intellectual in dis- 
tinction from esthetic. In the mere reading of a scientific treatise 
there is, indeed, no direct overt participation in action with an- 
other to produce consequences that are common in the sense of 
being immediately and personally shared. But there must be 
imaginative construction of the materials and operations which led 
the author to certain conclusions, and there must be agreement or 
disagreement with his conclusions as a consequence of following 
through conditions and operations that are imaginatively rein- 
stated. 

Connection with overt activities is in such a case indirect or 
mediated. But so far as definite grounded agreement or disagree- 
ment is reached, an attitude is formed which is a preparatory read- 
iness to act in a responsive way when the conditions in question 



THE EXISTENTIAL MATRIX OF INQUIRY 49 

or others similar to them actually present themselves. The con- 
nection with action in question is, in other words, with possible 
ways of operation rather than with those found to be actually and 
immediately required. 2 But preparation for possible action in sit- 
uations not as yet existent in actuality is an essential condition of, 
and factor in, all intelligent behavior. When persons meet to- 
gether in conference to plan in advance of actual occasions and 
emergencies what shall later be done, or when an individual delib- 
erates in advance regarding his possible behavior in a possible fu- 
ture contingency, something occurs, but more directly, the same 
sort as happens in understanding intellectually the meaning of a 
scientific treatise. 

I turn now to the positive implication of the fact that no sound, 
mark, product of art, is a word or part of language in isolation. 
Any word or phrase has the meaning which it has only as a mem- 
ber of a constellation of related meanings. Words as representa- 
tives are part of an inclusive code. The code may be public or 
private. A public code is illustrated in any language that is cur- 
rent in a given cultural group. A private code is one agreed upon 
by members of special groups so as to be unintelligible to those 
who have not been initiated. Between these two come argots of 
special groups in a community, and the technical codes invented 
for a restricted special purpose, like the one used by ships at sea. 
But in every case, a particular word has its meaning only in rela- 
tion to the code of which it is one constituent. The distinction 
just drawn between meanings that are determined respectively in 
fairly direct connection with action in situations that are present 
or near at hand, and meanings determined for possible use in re- 
mote and contingent situations, provides the basis upon which 
language codes as systems may be differentiated into two main 
kinds. 

While all language or symbol-meanings are what they are as 
parts of a system, it does not follow that they have been deter- 
mined on the basis of their fitness to be such members of a system; 
much less on the basis of their membership in a comprehensive 

2 Literature and literary habits are a strong force in building up that conception 
of separation of ideas and theories from practical activity which is discussed in 
ensuing chapters. 



50 INTRODUCTION: THE MATRIX OF INQUIRY 

system. The system may be simply the language in common 
use. Its meanings hang together not in virtue of their examined 
relationship to one another, but because they are current in the 
same set of group habits and expectations. They hang together 
because of group activities, group interests, customs and institu- 
tions. Scientific language, on the other hand, is subject to a test 
over and above this criterion. Each meaning that enters into the 
language is expressly determined in its relation to other members 
of the language system. In all reasoning or ordered discourse this 
criterion takes precedence over that instituted by connection 
with cultural habits. 

The resulting difference in the two types of language-meanings 
fundamentally fixes the difference between what is called com- 
mon sense and what is called science. In the former cases, the 
customs, the ethos and spirit of a group is the decisive factor in 
determining the system of meanings in use. The system is one in 
a practical and institutional sense rather than in an intellectual 
sense. Meanings that are formed on this basis are sure to contain 
much that is irrelevant and to exclude much that is required for 
intelligent control of activity. The meanings arc coarse, and 
many of them are inconsistent with each other from a logical 
point of view. One meaning is appropriate to action under cer- 
tain institutional group conditions; another, in some other situa- 
tion, and there is no attempt to relate the different situations to 
one another in a coherent scheme. In an intellectual sense, there 
are many languages, though in a social sense there is but one. This 
multiplicity of language-meaning constellations is also a mark of 
our existing culture. A word means one thing in relation to a 
religious institution, still another thing in business, a third thing 
in law, and so on. This fact is the real Babel of communication. 
There is an attempt now making to propagate the idea that educa- 
tion which indoctrinates individuals into some special tradition 
provides the way out of this confusion. Aside from the fact that 
there are in fact a considerable number of traditions and that se- 
lection of some one of them, even though that one be internally 
consistent and extensively accepted, is arbitrary, the attempt re- 
verses the theoretical state of the case. Genuine community of 
language or symbols can be achieved only through efforts that 



THE EXISTENTIAL MATRIX OF INQUIRY 51 

bring about community of activities under existing conditions. 
The ideal of scientific-language is construction of a system in 
which meanings are related to one another in inference and dis- 
course and where the symbols are such as to indicate the relation. 

I shall now introduce the word "symbol" giving it its significa- 
tion as a synonym for a word as a word, that is, as a meaning car- 
ried by language in a system, whether the system be of the loose 
or the intellectual rigorous kind. 3 The especial point in the intro- 
duction of the word "symbol" is to institute the means by which 
discrimination between what is designated by it and what is now 
often designated by sign may be instituted. What I have called 
symbols are often called "artificial signs" in distinction from what 
are called natural signs. 

IV. It is by agreement in conjoint action of the kind already 
described, that the word "smoke" stands in the English language 
for an object of certain qualities. In some other language the 
same vocable and mark may stand for something different, and 
an entirely different sound stand for "smoke." To such cases of 
representation the word "artificial signs" applies. When it is 
said that smoke as an actual existence points to, is evidence of, 
an existential fire, smoke is said to be a natural sign of fire. Simi- 
larly, heavy clouds of given qualities are a natural sign of prob- 
able rain, and so on. The representative capacity in question is 
attributed to things in their connection with one another, not to 
marks whose meaning depends upon agreement in social use. 
There is no doubt of the existence and the importance of the 
distinction designated by the words "natural" and "artificial" signs. 
But the fundamentally important difference is not brought out by 
these words. For reasons now to be given, I prefer to mark the 
difference by confining the application of sign to so-called "natural 
signs" — employing symbol to designate "artificial signs." 

The difference just stated is actual. But it fails to note the dis- 
tinctive intellectual property of what I call symbols. It is, so to 

3 This signification is narrower than the popular usage, according to which any- 
thing is a symbol that has representative emotional force even if that force be 
independent of its intellectual representational force. In this wider sense, a national 
flag, a crucifix, a mourning garb, etc., are symbols. The definition of the text is 
in so far arbitrary. But there is nothing arbitrary about the subject-matters to 
which the limited signification applies. 



52 INTRODUCTION: THE MATRIX OF INQUIRY 

speak, an incidental and external fact, logically speaking, that 
certain things are given representative function by social agree- 
ment. The fact becomes logically relevant only because of the 
possibility of free and independent development of meanings in 
discourse which arises when once symbols are instituted. A "nat- 
ural sign," by description, is something that exists in an acutal 
spatial-temporal context. Smoke, as a thing having certain ob- 
served qualities, is a sign of fire only when the thing exists and 
is observed. Its representative capacity, taken by itself, is highly 
restricted, for it exists only under limited conditions. The situa- 
tion is very different when the meaning "smoke" is embodied in 
an existence, like a sound or a mark on paper. The actual quality 
found in existence is then subordinate to a representative office. 
Not only can the sound be produced practically at will, so that 
we do not have to wait for the occurrence of the object; but, 
what is more important, the meaning when embodied in an indif- 
ferent or neutral existence is liberated with respect to its represent- 
ative function. It is no longer tied down. It can be related to 
other meanings in the language-system; not only to that of fire but 
to such apparently unrelated meanings as friction, changes of tem- 
perature, oxygen, molecular constitution, and, by intervening 
meaning-symbols, to the laws of thermodynamics. 

I shall, accordingly, in what follows, connect sign and signifi- 
cance ; symbol and meaning, respectively, with each other, in order 
to have terms to designate two different kinds of representative ca- 
pacity. Linguistically, the choice of terms is more or less arbi- 
trary, although sign and significance have a common verbal root. 
This consideration is of no importance, however, compared with 
the necessity of having some words by which to designate the two 
kinds of representative function. For purposes of theory the im- 
portant consideration is that existent things, as signs, are evidence 
of the existence of something else, this something being at the 
time inferred rather than observed. 

But words, or symbols, provide no evidence of any existence. 
Yet what they lack in this capacity they make up for in creation 
of another dimension. They make possible ordered discourse or 
reasoning. For this may be carried on without any of the exist- 
ences to which symbols apply being actually present: without, in- 



THE EXISTENTIAL MATRIX OF INQUIRY 53 

deed, assurance that objects to which they apply anywhere actu- 
ally exist, and, as in the case of mathematical discourse, without 
direct reference to existence at all. 

Ideas as ideas, hypotheses as hypotheses, would not exist were 
it not for symbols and meanings as distinct from signs and signifi- 
cances. The greater capacity of symbols for manipulation is of 
practical importance. But it pales in comparison with the fact 
that symbols introduce into inquiry a dimension different from 
that of existence. Clouds of certain shapes, size and color may 
signify to us the probability of rain; they portend rain. But the 
word cloud when it is brought into connection with other words 
of a symbol-constellation enable us to relate the meaning of being 
a cloud with such different matters as differences of temperature 
and pressures, the rotation of the earth, the laws of motion, and 
so on. 

The difference between sign-significance and symbol-meaning 
(in the sense defined) is brought out in the following incident. 4 
A visitor in a savage tribe wanted on one occasion "the word for 
Table. There were five or six boys standing around, and tapping 
the table with my forefinger I asked 'What is this?' One boy 
said it was dodela, another that it was an etanda, a third stated 
that it was bokali, & fourth that it was elamba y and the fifth said it 
was meza? After congratulating himself on the richness of the 
vocabulary of the language the visitor found later "that one boy 
had thought he wanted the word for tapping; another understood 
we were seeking the word for the material of which the table was 
made; another had the idea that we required the word for hard- 
ness; another thought we wished the name for that which covered 
the table; and the last . . . gave us the word meza> table." 

This story might have been quoted earlier as an illustration of 
the fact that there is not possible any such thing as a direct one- 
to-one correspondence of names with existential objects; that 
words mean what they mean in connection with conjoint activi- 
ties that effect a common, or mutually participated in, conse- 
quence. The word sought for was involved in conjoint activities 
looking to a common end. The act of tapping in the illustration 
was isolated from any such situation. It was, in consequence, 

4 Quoted by and from Ogden and Richards, The Meaning of Meaning, p. 174. 



54 INTRODUCTION: THE MATRIX OF INQUIRY 

wholly indeterminate in reference; it was no part of communica- 
tion, by which alone acts get significance and accompanying 
words acquire meaning. 5 For the point in hand, the anecdote il- 
lustrates the lack of any evidential status in relation to existence of 
the symbols or representative values that have been given the 
name "meanings." Without the intervention of a specific kind 
of existential operation they cannot indicate or discriminate the 
objects to which they refer. Reasoning or ordered discourse, 
which is defined by development of symbol-meanings in relation 
to one another, may (and should) provide a basis for performing 
these operations, but of itself it determines no existence. This 
statement holds no matter how comprehensive the meaning-system 
and no matter how rigorous and cogent the relations of meanings 
to one another. On the other hand, the story illustrates how, in 
case the right word had been discovered, the meaning symbolized 
would have been capable of entering into relations with any 
number of other meanings independently of the actual presence 
at any given time of the object table. Just as the sign-significance 
relation defines inference, so the relation of meanings that consti- 
tutes propositions defines implication in discourse, if it satisfies the 
intellectual conditions for which it is instituted. Unless there are 
words which mark off the two kinds of relations in their distinc- 
tive capacities and offices, with reference to existence, there is 
danger that two things as logically unlike as inference and impli- 
cation will be confused. As a matter of fact, the confusion, when 
inference is treated as identical with implication, has been a power- 
ful agency in creating the doctrinal conception that logic is purely 
formal — for, as has been said, the relation of meanings (carried 
by symbols) to one another is, as such, independent of existential 
reference. 

V. So far the word "relation" has been rather indiscriminately 
employed. The discussion has now reached a point where it is 
necessary to deal with the ambiguity of the word as it is used not 

5 Another aspect of the same general principle, not directly connected with 
language, is brought out later in consideration of the meaning of any demon- 
strated object in relation to "this" 

b A farther important logical aspect of this matter is dealt with below in the 
necessity of distinguishing judgment from propositions, and Involvement from 
implication. 



THE EXISTENTIAL MATRIX OF INQUIRY 55 

merely in ordinary speech but in logical texts. The word "rela- 
tion" is used to cover three very different matters which in the 
interest of a coherent logical doctrine must be discriminated. (1) 
Symbols are "related" directly to one another; (2) they are "re- 
lated" to existence by the mediating intervention of existential 
operations; (3) existences are "related" to one another in the evi- 
dential sign-signified function. That these three modes of "rela- 
tion" are different from one another and that the use of one and 
the same word tends to cover up the difference and thereby create 
doctrinal confusion, is evident. 

In order to avoid, negatively, the disastrous doctrinal confusion 
that arises from the ambiguity of the word relation, and in order 
to possess, positively, linguistic means of making clear the logical 
nature of the different subject-matters under discussion, I shall 
reserve the word relation to designate the kind of "relation" which 
symbol-meanings bear to one another as symbol-meanings. I shall 
use the term reference to designate the kind of relation they sus- 
tain to existence; and the words connection (and involvement) to 
designate that kind of relation sustained by things to one another 
in virtue of which inference is possible. 

The differences, when once pointed out, should be so obvious 
as hardly to require illustration. Consider, however, propositions 
of mathematical physics. ( 1 ) As propositions they form a system 
of related symbol-meanings that may be considered and devel- 
oped as such. (2) But as propositions of physics, not of mere 
mathematics, they have reference to existence; a reference which 
is realized in operations of application. (3) The final test of valid 
reference or applicability resides in the connections that exist 
among things. Existential involvement of things with one another 
alone warrants inference so as to enable further connections among 
things themselves to be discovered. 

The question may be raised whether meaning-relations in dis- 
course arise before or after significance-connections in existence. 
Did we first infer and then use the results to engage in discourse? 
Or did relations of meanings, instituted in discourse, enable us to 
detect the connections in things in virtue of which some things 
are evidential of other things? The question is rhetorical in that 
the question of historical priority cannot be settled. The question 



56 INTRODUCTION: THE MATRIX OF INQUIRY _ 

is asked, however, in order to indicate that in any case ability to 
treat things as signs would not go far did not symbols enable us 
to mark and retain just the qualities of things which are the 
ground of inference. Without, for example, words or symbols 
that discriminate and hold on to the experienced qualities of sight 
and smell that constitute a thing "smoke," thereby enabling it to 
serve as a sign of fire, we might react to the qualities in question 
in animal-like fashion and perform activities appropriate to them. 
But no inference could be made that was not blind and blunder- 
ing. Moreover, since what is inferred, namely fire, is not present 
in observation, any anticipation that could be formed of it would 
be vague and indefinite, even supposing an anticipation could 
occur at all. If we compare and contrast the range and the depth 
of the signifying capacity of existential objects and events in a 
savage and a civilized group and the corresponding power of 
inference, we find a close correlation between it and the scope and 
the intimacy of the relations that obtain between symbol-meanings 
in discourse. Upon the whole, then, it is language, originating as 
a medium of communication in order to bring about deliberate co- 
operation and competition in conjoint activities, that has conferred 
upon existential things their signifying or evidential power. 

VI. We are thus brought back to the original problem: namely, 
transformation of animal activities into intelligent behavior having 
the properties which, when formulated, are logical in nature. As- 
sociated behavior is characteristic not only of plants and animals, 
but of electrons, atoms and molecules; as far as we know of every- 
thing that exists in nature. Language did not originate association, 
but when it supervened, as a natural emergence from previous 
forms of animal activity, it reacted to transform prior forms and 
modes of associated behavior in such a way as to give experience 
a new dimension. 

1. "Culture" and all that culture involves, as distinguished from 
"nature," is both a condition and a product of language. Since 
language is the only means of retaining and transmitting to subse- 
quent generations acquired skills, acquired information and ac- 
quired habits, it is the latter. Since, however, meanings and the 
significance of events differ in different cultural groups, it is also 
the former. 



THE EXISTENTIAL MATRIX OF INQUIRY 57 

2. Animal activities, such as eating and drinking, searching for 
food, copulation, etc., acquire new properties. Eating food be- 
comes a group festival and celebration; procuring food, the art of 
agriculture and exchange; copulation passes into the institution of 
the family. 

3. Apart from the existence of symbol-meanings the results of 
prior experience are retained only through strictly organic modi- 
fications. Moreover, these modifications once made, tend to be- 
come so fixed as to retard, if not to prevent, the occurrence of 
further modifications. The existence of symbols makes possible 
deliberate recollection and expectation, and thereby the institu- 
tion of new combinations of selected elements of experiences hav- 
ing an intellectual dimension. 

4. Organic biological activities end in overt actions, whose con- 
sequences are irretrievable. When an activity and its consequences 
can be rehearsed by representation in symbolic terms, there is no 
such final commitment. If the representation of the final con- 
sequence is of unwelcome quality, overt activity may be fore- 
gone, or the way of acting be replanned in such a way as to avoid 
the undesired outcome. 7 

These transformations and others which they suggest, are not 
of themselves equivalent to accrual of logical properties to behav- 
ior. But they provide requisite conditions for it. The use of 
meaning-symbols for institution of purposes or ends-in-view, for 
deliberation, as a rehearsal through such symbols of the activities by 
which the ends may be brought into being, is at least a rudimentary 
form of reasoning in connection with solution of problems. The 
habit of reasoning once instituted is capable of indefinite develop- 
ment on its own account. The ordered development of mean- 
ings in their relations to one another may become an engrossing 
interest. When this happens, implicit logical conditions are made 
explicit and then logical theory of some sort is born. It may be 
imperfect; it will be imperfect from the standpoint of the in- 
quiries and symbol-meanings that later develop. But the first step, 
the one that costs and counts, was taken when some one began to 

7 Generalizing beyond the strict requirements of the position outlined, I would 
say that I am not aware of any so-called merely "mental" activity or result that 
cannot be described in the objective terms of an organic activity modified and 
directed by symbols-meaning, or language, in its broad sense. 



58 INTRODUCTION: THE MATRIX OF INQUIRY^ 

reflect upon language, upon logos, in its syntactical structure and 
its wealth of meaning contents. Hypostization of Logos was the 
first result, and it held back for centuries the development of in- 
quiries of a kind that are competent to deal with the problems of 
the existent world. But the hypostization was, nevertheless, a 
tribute to the power of language to generate reasoning and, 
through application of the meanings contained in it, to confer 
fuller and more ordered significance upon existence. 

In later chapters we shall consider in some detail how- a logic 
of ordered discourse, a logic that gathered in a system the rela- 
tions which hold meanings consistently together in discourse, was 
taken to be the final model of logic and thereby obstructed the 
development of effective modes of inquiry into existence, pre- 
venting the necessary reconstruction and expansion of the very 
meanings that were used in discourse. For when these meanings 
in their ordered relations to one another were taken to be final in 
and of themselves, they were directly superimposed upon nature. 
The necessity of existential operations for application of mean- 
ings to natural existence was ignored. This failure reacted into the 
system of meanings as meanings. The result was the belief that 
the requirements of rational discourse constitute the measure of 
natural existence, the criterion of complete Being. It is true that 
logic emerged as the Greeks became aware of language as LogOvS 
with the attendant implication that a system of ordered meanings 
is involved. 

This perception marked an enormous advance. But it suffered 
from two serious defects. Because of the superior status as- 
signed to forms of rational discourse, they were isolated from 
the operations by means of which meanings originate, function 
and are tested. This isolation was equivalent to the hypostiza- 
tion of Reason. In the second place, the meanings that w r ere 
recognized were ordered in a gradation derived from and controlled 
by a class-structure of Greek society. The means, procedures 
and kinds of organization that arose from active or "practical" 
participation in natural processes were given a low rank in the 
hierarchy of Being and Knowing. The scheme of knowledge 
and of Nature became, without conscious intent, a mirror of a 
social order in which craftsmen, mechanics, artisans generally, 



THE EXISTENTIAL MATRIX OF INQUIRY 59 

held a low position in comparison with a leisure class. Citizens 
as citizens were also occupied with doing, a doing instigated by 
need or lack. While possessed of a freedom denied to the artisan 
class, they were also taken to fail in completely self-contained and 
self-sufficient activity. The latter was exemplified only in the 
exercise of Pure Reason untainted by need for anything outside it- 
self and hence independent of all operations of doing and making. 
The historic result was to give philosophic, even supposedly onto- 
logical, sanction to the cultural conditions which prevented the 
utilization of the immense potentialities for attainment of knowl- 
edge that were resident in the activities of the arts— resident in 
them because they involve operations of active modification of exist- 
ing conditions which contain the procedures constituting the ex- 
perimental method when once they are employed for the sake of 
obtaining knowledge, instead of being subordinated to a scheme 
of uses and enjoyments controlled by given socio-cultural con- 
ditions. 



CHAPTER IV 

COMMON SENSE AND SCIENTIFIC INQUIRY 



-rj- -7-PON the biological level, organisms have to respond to 
' ' ' conditions about them in ways that modify those condi- 



u 



tions and the relations of organisms to them so as to re- 
store the reciprocal adaptation that is required for the maintenance 
of life-functions. Human organisms are involved in the same sort 
of predicament. Because of the effect of cultural conditions, the 
problems involved not only have different contents but arc capable 
of statement as problems so that inquiry can enter as a factor 
in their resolution. For in a cultural environment, physical condi- 
tions are modified by the complex of customs, traditions; occupa- 
tions, interests and purposes which envelops them. .Modes of re- 
sponse are correspondingly transformed. They avail themselves of 
the significance which things have acquired, and of the meanings 
provided by language. Obviously, rocks as minerals signify some- 
thing more in a group that has learned to work iron than it signifies 
either to sheep and tigers or to a pastoral or agricultural group. 
The meanings of related symbols, which form the language of a 
group, also, as was shown in the last chapter, introduce a new type 
of attitudes and hence of modes of response. I shall designate the 
environment in which human beings are directly involved the 
common sense environment or "world," and inquiries that take 
place in making the required adjustments in behavior common 
sense inquiries. 

As is brought out later, the problems that arise in such situations 
of interaction may be reduced to problems of the use and enjoy- 
ment of the objects, activities and products, material and ideologi- 
cal, (or "ideal") of the world in which individuals live. Such 
inquiries are, accordingly, different from those which have knowl- 
edge as their goal. The attainment of knowledge of some things 
is necessarily involved in common sense inquiries, but it occurs 

60 



COMMON SENSE AND SCIENTIFIC INQUIRY 61 

for the sake of settlement of some issue of use and enjoyment, 
and not, as in scientific inquiry, for its own sake. In the latter, 
there is no direct involvement of human beings in the immediate 
environment — a fact which carries with it the ground of distin- 
guishing the theoretical from the practical. 

The use of the term common sense is somewhat arbitrary from 
a linguistic point of view. But the existence of the kinds of situa- 
tions referred to and of the kind of inquiries that deal with the 
difficulties and predicaments they present cannot be doubted. 
They are those which continuously arise in the conduct of life 
and the ordering of day-by-day behavior. They are such as con- 
stantly arise in the development of the young as they learn to make 
their way in the physical and social environments in which they 
live; they occur and recur in the life-activity of every adult, 
whether farmer, artisan, professional man, law-maker or adminis- 
trator; citizen of a state, husband, wife, or parent. On their very 
face they need to be discriminated from inquiries that are distinc- 
tively scientific, or that aim at attaining confirmed facts, "laws" 
and theories. 

They need, accordingly, to be designated by some distinctive 
word, and common sense is used for that purpose. Moreover, the 
term is not wholly arbitrary even from the standpoint of linguis- 
tic usage. In the Oxford Dictionary, for example, is found the 
following definition of common sense: "Good sound practical 
sense; combined tact and readiness in dealing with the ordinary 
affairs of life." Common sense in this signification applies to be- 
havior in its connection with the significance of things. 

There is, clearly, a distinctively intellectual content involved; 
good sense is, in ordinary language, good judgment. Sagacity is 
power to discriminate the factors that are relevant and important 
in significance in given situations; it is power of discernment; in 
a proverbial phrase, ability to tell a hawk from a hernshaw, chalk 
from cheese, and to bring the discriminations made to bear upon 
what is to be done and what is to be abstained from, in the "ordi- 
nary affairs of life." That which, in the opening paragraphs, was 
called the mode of inquiry dealing with situations of use and en- 
joyment, is, after all, but a formal way of saying what the dic- 
tionary states in its definition of common sense. 



62 INTRODUCTION: THE MATRIX OF INQUIRY 

There is, however, another dictionary definition: 'The general 
sense, feeling, judgment of mankind or a community." It is in 
this sense that we speak of the deliverances of common sense as 
if they were a body of settled truths. It applies not to things in 
their significance but to weaning* accepted. When the Scottish 
school of Reid and Stewart erected "common sense" into an ulti- 
mate authority and arbiter of philosophic questions, they were 
carrying this signification to its limit. The reference to practical 
sagacity in dealing with problems of response and adaptation in 
use and enjoyment has now gone into the background. "Com- 
mon" now means "general" It designates the conceptions and 
beliefs that are currently accepted without question by a given 
group or by mankind in general. They are common in the sense 
of being widely, if not universally, accepted. They are sense, in 
the way in which we speak of the "sense of a meeting" and in 
which we say things do or do not "make sense." They have some- 
thing of the same ultimacy and immediacy for a group that 
"sensation" and "feeling" have for an individual in his contact 
with surrounding objects. It is a commonplace that every cultural 
group possesses a set of meanings which are so deeply embedded 
in its customs, occupations, traditions and ways of interpreting 
its physical environment and group-life, that they form the basic 
categories of the language-system by which details are interpreted. 
Hence they are regulative and "normative" of specific beliefs and 
judgments. 

There is a genuine difference between the two meanings of 
common sense. But from the standpoint of a given group there 
is a definite deposit of agreement. They are both of them con- 
nected with the conduct of life in relation to an existing environ- 
ment: one of them in judging the significance of things and events 
with reference to what should be done; the other, in the ideas that 
are used to direct and justify activities and judgments. Tabus 
are, first, customary ways of activities. To us they arc mistaken 
rather than sagacious ways of action. But the system of meanings 
embodied in the language that carries tradition gives them authority 
in such highly practical matters as the eating of food and the be- 
havior that is proper in the presence of chieftains and members of 
the family configuration, so that they control the relations of males 



COMMON SENSE AND SCIENTIFIC INQUIRY 63 

and females and persons of various kinship degrees. To us, such 
conceptions and beliefs are highly impractical; to those who held 
them they were matters of higher practical importance than were 
special modes of behavior in dealing with particular objects. For 
they set the standards for judging the latter and acting in reference 
to them. It is possible today, along with our knowledge of the 
enormous differences that characterize various cultures, to find 
some unified deposit of activities and of meanings in the "common 
sense and feeling of mankind" especially in matters of basic social 
cohesion. 

In any case, the difference between the two meanings may be 
reduced, without doing violence to the facts, to the difference be- 
tween phases and aspects of special practical situations that are 
looked into, questioned and examined with reference to what 
may or should be done at a particular time and place and the 
rules and precepts that are taken for granted in reaching all con- 
clusions and in all socially correct behavior. Both are concerned, 
one directly and the other indirectly, with "the ordinary affairs 
of life," in the broad sense of life. 

I do not suppose that a generalization of the inquiries and con- 
clusions of this type under the caption of "use and enjoyment" 
needs much exposition for its support. Use and enjoyment are 
the ways in which human beings are directly connected with the 
world about them. Questions of food, shelter, protection, de- 
fense, etc., are questions of the use to be made of materials of the 
environment and of the attitudes to be taken practically towards 
members of the same group and to other groups taken as wholes. 
Use, in turn, is for the sake of some consummation or enjoyment. 
Some things that are far beyond the scope of direct use, like stars 
and dead ancestors, are objects of magical use, and of enjoyment in 
rites and legends. If we include the correlative negative ideas of 
disuse, of abstinence from use, and toleration and suffering, prob- 
lems of use and enjoyment may be safely said to exhaust the do- 
main of common sense inquiry. 

There is direct connection between this fact and the concern 
of common sense with the qualitative. It is by discernment of 
qualities that the fitness and capacity of things and events for use 
is decided; that proper foodstuffs, for example, are told or dis- 



64 INTRODUCTION: THE MATRIX OF INQUIRY 

criminated from those that are unfit, poisonous or tabued. That 
enjoyment-suffering is qualitative through and through and is con- 
cerned with situations in their pervasive qualitative character, is 
almost too obvious for mention. Furthermore, the operations and 
responses that are engaged in use and enjoyment of situations are 
qualitatively marked off. Tanning skins is a process qualitatively 
different from that of weaving baskets or shaping clay into jars; 
the rites that are responsive to death are qualitatively different 
from those appropriate to birth and weddings. Inferiors, superiors 
and equals are treated in modes of greeting and approach that are 
qualitatively unlike. 

The reason for calling attention to these commonplace facts is 
that they bring out the basic difference between the subject-mat- 
ters characteristic of common sense and of scientific inquiries; and 
they also indicate the differences between the problems and pro- 
cedures of inquiry that are characteristic of common sense in dif- 
ferent stages of culture. I shall first consider the latter point 
Common sense in respect to both its content of ideas and beliefs, 
and its methods of procedure, is anything but a constant. Both 
its content and its methods alter from time to time not merely in 
detail but in general pattern. Every invention of a new tool and 
utensil, every improvement in technique, makes some difference 
in what is used and enjoyed and in the inquiries that arise with 
reference to use and enjoyment, with respect to both significance 
and meaning. Changes in the regulative scheme of relations within 
a group, family, clan or nation, react even more intensively into 
some older system of uses and enjoyments. 

One has only to note the enormous differences in the contents 
and methods of common sense in modes of life that are respectively 
dominantly nomadic, agricultural and industrial. Much that was 
once taken without question as a matter of common sense is for- 
gotten or actively condemned. Other old conceptions and con- 
victions continue to receive theoretical assent and strong emotional 
attachment because of their prestige. But they have little hold 
and application in the ordinary affairs of life. For example, ideas 
and practices which, in primitive tribes, were interwoven with 
practically every concern of ordinary affairs, are later relegated 
to a separate domain, religious or esthetic. 



COMMON SENSE AND SCIENTIFIC INQUIRY 65 

The business of one age becomes the sport and amusement of 
another age. Even scientific theories and interpretations continue 
to be affected by conceptions that have ceased to be determinative 
in the actual practice of inquiry. The special bearing of the fact 
that "common sense" is anything but a constant upon logical for- 
mulations, will concern us in the sequel. Here it is enough to call 
attention to a point which will later receive detailed examination: 
namely, the very fitness of the Aristotelian logical organon in 
respect to the culture and common sense of a certain group in the 
period in which it was formulated unfits it to be a logical formu- 
lation of not only the science but even of the common sense of the 
present cultural epoch. 

I recur now to the bearing of the fact that common sense u> 
quiries are concerned with qualitative matter and operations upon 
their distinction from scientific inquiries. Fundamentally, the 
distinction is that brought out in the previous chapter: Namely, 
that between significances and meanings that are determined in 
reference to pretty direct existential application and those that 
are determined on the ground of their systematic relations of co- 
herence and consistency with one another. All that the present 
mode of statement adds is that, in the first case, "existential appli- 
cation" means application in qualitative use and enjoyment of the 
environment. On the other hand, both the history of science and 
the present state of science prove that the goal of the systematic 
relationship of facts and conceptions to one another is dependent 
upon elimination of the qualitative as such and upon reduction to 
non-qualitative formulation. 

The problem of the relation of the domain of common sense to 
that of science has notoriously taken the form of opposition of 
the qualitative to the non-qualitative; largely, but not exclusively, 
the quantitative. The difference has often been formulated as the 
difference between perceptual material and a system of conceptual 
constructions. In this form it has constituted, in recent centuries, 
the chief theme of epistemology and metaphysics. From the 
standpoint that controls the present discussion, the problem is not 
epistemological (save as that word means the logical) nor is it 
metaphysical or ontological. In saying that it is logical, it is 
affirmed that the question at issue is that of the relation to each 



68 INTRODUCTION: THE MATRIX OF INQUIRY _ 

event as such but only to determine what it signifies with respect 
to the way in which the entire situation should be dealt with, the 
opposition and conflict do not arise. The object or event in ques- 
tion is perceived as part of the environing world, not in and by 
itself; it is rightly (validly) perceived if and when it acts as clew 
and guide in use-enjoyment. We live and act in connection with 
the existing environment, not in connection with isolated objects, 
even though a singular thing may be crucially significant in decid- 
ing how to respond to total environment. 

Recurring to the main topic, it is to be remarked that a situation 
is a whole in virtue of its immediately pervasive quality. When we 
describe it from the psychological side, we have to say that the 
situation as a qualitative whole is sensed or felt. Such an expres- 
sion is, however, valuable only as it is taken negatively to indicate 
that it is not, as such, an object in discourse. Stating that it is felt 
is wholly misleading if it gives the impression that the situation is 
a feeling or an emotion or anything mentalistic. On the contrary, 
feeling, sensation and emotion have themselves to be identified and 
described in terms of the immediate presence of a total qualitative 
situation. 

The pervasively qualitative is not only that which binds all con- 
stituents into a whole but it is also unique; it constitutes in each 
situation an individual situation, indivisible and unduplicablc. Dis- 
tinctions and relations are instituted ivitlmz a situation; they are 
recurrent and repeatable in different situations. Discourse that is 
not controlled by reference to a situation is not discourse, but a 
meaningless jumble, just as a mass of pied type is not a font much 
less a sentence. A universe of experience is the precondition of a 
universe of discourse. Without its controlling presence, there is 
no way to determine the relevancy, weight or coherence of any 
designated distinction or relation. The universe of experience 
surrounds and regulates the universe of discourse but never ap- 
pears as such within the latter. It may be objected that what was 
previously said contradicts this statement. For we have been dis- 
coursing about universes of experience and situations, so that the 
latter have been brought within the domain of symbols. The ob- 
jection, when examined, serves to elicit an important considera- 
tion. It is a commonplace that a universe of discourse cannot be a 



COMMON SENSE AND SCIENTIFIC INQUIRY 69 

term or element within itself. One universe of discourse may, 
however, be a term of discourse within another universe. The 
same principle applies in the case of universes of experience. 

The reader, whether he agrees or not with what has been said, 
whether he understands it or not, has, as he reads the above 
passages, a uniquely qualified experienced situation, and his re- 
flective understanding of what is said is controlled by the nature 
of that immediate situation. One cannot decline to have a situa- 
tion for that is equivalent to having no experience, not even one of 
disagreement. The most that can be refused or declined is the 
having of that specific situation in which there is reflective recogni- 
tion (discourse) of the presence of former situations of the kind 
stated. This very declination is, nevertheless, identical with initia- 
tion of another encompassing qualitative experience as a unique 
whole. 

In other words, it "would be a contradiction if I attempted to 
demonstrate by means of discourse, the existence of universes of 
experience. It is not a contradiction by means of discourse to 
invite the reader to have for himself that kind of an immediately 
experienced situation in which the presence of a situation as a 
universe of discourse is seen to be the encompassing and regulat- 
ing condition of all discourse. 

There is another difficulty in grasping the meaning of what has 
been said. It concerns the use of the word "quality." The word 
is usually associated with something specific, like red, hard, sweet; 
that is, with distinctions made within a total experience. The 
intended contrasting meaning may be suggested, although not 
adequately exemplified, by considering such qualities as are desig- 
nated by the terms distressing, perplexing, cheerful, disconsolate. 
For these words do not designate specific qualities in the way in 
which hard, say, designates a particular quality of a rock. For 
such qualities permeate and color all the objects and events that are 
involved in an experience. The phrase "tertiary qualities," hap- 
pily introduced by Santayana, does not refer to a third quality like 
in kind to the "primary" and "secondary" qualities of Locke and 
merely happening to differ in content. For a tertiary quality 
qualifies all the constituents to which it applies in thoroughgoing 
fashion. 



70 INTRODUCTION: THE MATRIX OF INQUIRY _ 

Probably the meaning of quality, in the sense in which quality is 
said to pervade all elements and relations that are or can be in- 
stituted in discourse and thereby to constitute them an individual 
whole, can be most readily apprehended by referring to the 
esthetic use of the word. A painting is said to have quality, or a 
particular painting to have a Titian or Rembrandt quality. The 
word thus used most certainly does not refer to any particular line, 
color or part of the painting. It is something that affects and 
modifies all the constituents of the picture and all of their relations. 
It is not anything that can be expressed in words for it is something 
that must be had. Discourse may, however, point out the qualities, 
lines and relations by means of which pervasive and unifying 
quality is achieved. But so far as this discourse is separated from 
having the immediate total experience, a reflective object takes 
the place of an esthetic one. Esthetic experience, in its emphatic 
sense, is mentioned as a way of calling attention to situations and 
universes of experience. The intended force of the illustration 
would be lost if esthetic experience as such were supposed to ex- 
haust the scope and significance of a ''situation." As has been said, 
a qualitative and qualifying situation is present as the background 
and the control of every experience. It was for a similar reason 
that it was earlier stated that reference to tertiary qualities was not 
adequately exemplary. For such qualities as arc designated by 
"distressing," "cheerful," etc., are general, while the quality of 
distress and cheer that marks an existent situation is not general but 
is unique and inexpressible in words. 

I give one further illustration from a different angle of approach. 
It is more or less a commonplace that it is possible to carry on 
observations that amass facts tirelessly and yet the observed "facts" 
lead nowhere. On the other hand, it is possible to have the work 
of observation so controlled by a conceptual framework fixed in 
advance that the very things which are genuinely decisive in the 
problem in hand and its solution, are completely overlooked. 
Everything is forced into the predetermined conceptual and the- 
oretical scheme. The way, and the only way, to escape these two 
evils, is sensitivity to the quality of a situation as a whole. In 
ordinary language, a problem must be felt before it can be stated. 
If the unique quality of the situation is had immediately, then there 



COMMON SENSE AND SCIENTIFIC INQUIRY 71 

is something that regulates the selection and the weighing of 
observed facts and their conceptual ordering. 

The discussion has reached the point where the basic problem of 
the relation of common sense material and methods to that of 
scientific subject-material and method, can be explicitly discussed. 
In the first place, science takes its departure of necessity from the 
qualitative objects, processes, and instruments of the common 
sense world of use and concrete enjoyments and sufferings. The 
scientific theory of colors and light is extremely abstract and 
technical. But it is about the colors and light involved in every- 
day affairs. Upon the common sense level, light and colors are 
not experienced or inquired into as things in isolation nor yet as 
qualities of objects viewed in isolation. They are experienced, 
weighed and judged in reference to their place in the occupations 
and arts (including social ceremonial arts as well as fine arts) the 
group carries on. Light is a dominant factor in the daily routine 
of rising from sleep and going about one's business. Differences 
in the duration of the light of sun and moon interpenetrate almost 
every tribal custom. Colors are signs of what can be done and of 
how it should be done in some inclusive situation — such as, judg- 
ing the prospects of the morrow's weather; selection of appropriate 
clothing for various occasions; dyeing, making rugs, baskets and 
jars; and so on in diverse ways too obvious and tedious to enumer- 
ate. They play their part either in practical decisions and activities 
or in enjoyed celebrations, dances, wakes, feasts, etc. What holds 
of light and color applies to all objects, events and qualities that 
enter into everyday common sense affairs. 

Gradually and by processes that are more or less tortuous and 
originally unplanned, definite technical processes and instru- 
mentalities are formed and transmitted. Information about things, 
their properties and behaviors, is amassed, independently of any 
particular immediate application. It becomes increasingly remote 
from the situations of use and enjoyment in which it originated. 
There is then a background of materials and operations available 
for the development of what we term science, although there is still 
no sharp dividing line between common sense and science. For 
purposes of illustration, it may be supposed that primitive astron- 
omy and primitive methods of keeping track of time (closely con- 



72 INTRODUCTION: THE MATRIX OF INQUIRY 

nected with astronomical observations) grew out of the practical 
necessities of groups with herds in care of animals with respect to 
mating and reproduction, and of agricultural groups with reference 
to sowing, tilling and reaping. Observation of the change of 
position of constellations and stars, of the relation of the length of 
daylight to the sun's place in relation to the constellations along 
the line of the equinox provided the required information. In- 
strumental devices were developed in order that the observations 
might be made; definite techniques for using the instruments 
followed. 

Measurement of angles of inclination and declination was a 
practical part of meeting a practical need. The illustration is, 
from a historical point of view, more or less speculative. But 
something of this general kind certainly effected the transition 
from what we call common sense to what we call science. If we 
were to take the practical needs of medicine in healing the sick 
and dealing with wounds, in their relation to the growth of 
physiological and anatomical knowledge, the case would be even 
clearer. In the early history of Greek reflective thought, art, or 
techne, and science, were synonymous. 

But this is not the whole of the story. Oriental cultures, 
especially the Assyrian, Babylonian and Egyptian, developed a 
division between "lower" and "higher" techniques and kinds of 
knowledge. The lower, roughly speaking, was in possession of 
those who did the daily practical work; carpentering, dyeing, 
weaving, making pottery, trading, etc. The higher came to be the 
possession of a special class, priests and the successors of primitive 
medicine men. Their knowledge and techniques were "higher" 
because they were concerned with what were supposed to be 
matters of ultimate concern; the welfare of the people and 
especially its rulers — and this welfare involved transactions with 
the powers that ruled the universe. Their kind of practical 
activity was so different from that of artisans and traders, the ob- 
jects involved were so different, the social status of the persons 
engaged in carrying on the activities in question was so enormously 
different, that the activity of the guardians and administrators of 
the higher knowledge and techniques was not "practical" in the 
sense of practical that applied to the ordinary useful worker. 



COMMON SENSE AND SCIENTIFIC INQUIRY 73 

These facts contained dualism in embryo, indeed in more or less 
mature form. This, when it was reflectively formulated, became 
the dualism of the empirical and rational, of theory and practice, 
and, in our own day, of common sense and science. 1 

The Greeks were much less subject to ecclesiastic and autocratic 
political control than were the peoples mentioned. The Greeks 
are pointed to with considerable justice as those who freed thought 
and knowledge from external control. But in one fundamentally 
important way they fixed, for subsequent intellectual history, the 
division just mentioned — although changing its direction and in- 
terpretation. Science and philosophy (which were still one) 
constituted the higher form of knowledge and activity. It alone 
was "rational" and alone deserved the names of knowledge and of 
activity that was "pure" because liberated from the constraints of 
practice. Experiential knowledge was confined to the artisan and 
trader, and their activity was "practical" because it was concerned 
with satisfaction of needs and desires — most of the latter, as in the 
case of the trader, being base and unworthy anyway. 

The free citizen was not supposed to engage in any of these 
pursuits but to devote himself to politics and the defense of the 
city-state. Although the scientist-philosopher was compelled by 
constraint of the body to give some time and thought to satisfaction 
of wants, as a scientist-philosopher he was engaged in exercising his 
reason upon rational objects, thereby attaining the only possible 
complete freedom and perfect enjoyment. The definitely socio- 
practical division between workers and non-citizens who were 
servile, and the members of the leisure class who were free citizens, 
was converted by philosophic formulation into a division between 
practice and theory, experience and reason. Strictly scientific- 
philosophic knowledge and activity were finally conceived to be 
supra-social as well as supra-empirical. They connected those who 
pursued them with the divine and cut them off from their fellows. 

I have engaged in what seems to be a historical excursus not 
for the sake of giving historical information but in order to indi- 
cate the origin of the distinction between empirical knowledge 
and practice on one hand and rational knowledge and pure 
activity on the other; between knowledge and practice that are 

^•See L. Hogben, Mathematics for the Millions, Ch. 1. 



74 INTRODUCTION: THE MATRIX OF INQUIRY 

admittedly of social origin and intent and the insight and activity 
that were supposed to have no social and practical bearings. This 
origin is itself social-cultural. Such is the irony of the situation. 
Relatively free as were the minds of Greek thinkers, momentous as 
were their accomplishments in certain directions, after Greek 
culture ceased to be a living thing and its products were carried 
over into different cultures, the inheritance from the Greeks be- 
came an incubus upon the progress of experience and of science, 
save in mathematics. Even in the latter field it kept mathematics 
for a long time subservient to strictly geometrical formulation. 

The later revival of genuine science undoubtedly drew stimulus 
and inspiration from the products of Greek thought. But these 
products were reanimated by contact and interaction with just the 
things of ordinary experience and the instruments of use in 
practical arts which in classic Greek thought were supposed to 
contaminate the purity of science. There was a return to the 
conditions and factors mentioned earlier: qualitative materials, 
processes and instruments. Phenomena of heat, light and electricity 
became matters to be experienced under controlled conditions 
instead of matters to receive rational formulation through pure 
intellect. The lens and compass and a multitude of the tools and 
processes of the practical arts were borrowed and adapted to the 
needs of scientific inquiry. The ordinary processes that had long 
been at home in the arts, weakening and intensifying, combining 
and separating, dissolving and evaporating, precipitating and in- 
fusing, heating and cooling, etc. etc., were no longer scorned. 
They were adopted as means of finding out something about 
nature, instead of being employed only for the sake of accomplish- 
ing objects of use and enjoyment. 

Symbolic instrumentalities, especially, underwent tremendous 
reconstruction; they were refined as well as expanded. On one 
hand they were constructed and related together on the basis of 
their applicability, through operations, to existence, and they were 
freed, on the other hand, from reference to direct application in 
use and enjoyment. The physical problems that emerged in 
pursuit of experiential knowledge of nature thus required and 
evoked new symbolic means of registration and manipulation. 
Analytic geometry and calculus became primary modes of concep- 



COMMON SENSE AND SCIENTIFIC INQUIRY IS 

tual response as quantity, change and motion were found to be not 
irrational accidents but the keys with which to solve the mysteries 
of natural existence. Language was, nonetheless, an old and 
familiar qualitative achievement. The most exact comprehensive 
mathematical language hardly compares as an achievement with 
the creation of intelligible speech by primitive peoples. Finally, 
the test of the validity of conceptions formulated and developed in 
rational discourse was found to reside in their applicability to 
existential qualitative material. They were no longer taken to be 
"true" as constituents of rational discourse in isolation but valid in 
the degree in which they were capable of organizing the qualitative 
materials of common sense and of instituting control over them. 
Those semantic-conceptual constructions that indicate with the 
greatest degree of defmiteness the way in which they are to be 
applied are, even as conceptions, the most truly rational ones. At 
every point in the practice of scientific inquiry, the old separation 
between experience and reason, between theory and doing, was 
destroyed. 

In consequence, the contents and techniques of common sense 
underwent a revolutionary change. It was noted earlier that com- 
mon sense is not a constant. But the most revolutionary change it 
has ever undergone is that effected by the infiltration and incor- 
poration of scientific conclusions and methods into itself. Even 
the procedures and materials that are connected with elementary 
environmental conditions of life, such things as food, clothing, 
shelter and locomotion, have undergone tremendous transforma- 
tion, while unprecedented needs and unprecedented powers of 
satisfying them have also emerged. The effect of the embodiment 
of science in the common sense world and the activities that deal 
with it in the domain of human relationships is as great as that which 
has taken place in relation to physical nature. It is only necessary to 
mention the social changes and problems that have arisen from the 
new technologies of production and distribution of goods and 
services. For these technologies are the direct product of the new 
science. To relate in detail the ways in which science has affected 
the area of common sense in respect to the relationships of person 
to person, group to group, people to people, would be to relate 
the story of social change in the last few centuries. Applications 



76 INTRODUCTION: THE MATRIX OF INQUIRY 

of science in revolutionizing the forces and conditions of produc- 
tion, distribution and communication have of necessity tremen- 
dously modified the conditions under which human beings live 
and act in connection with one another, whether the conditions be 
those of interchange and friendly association or of opposition and 
war. 

It is not intimated that the incorporation of scientific conclusions 
and operations into the common sense attitudes, beliefs and intel- 
lectual methods of what is now taken for granted as matters of 
common sense is as yet complete or coherent. The opposite is the 
case. In the most important matters the effect of science upon the 
content and procedures of common sense has been disintegrative. 
This disintegrative influence is a social, not a logical, fact. But 
it is the chief reason why it seems so easy, so "natural/' to make a 
sharp division between common sense inquiry and its logic and 
scientific inquiry and its logic. 

Two aspects of the disintegration which creates the semblance 
of complete opposition and conflict will be noted. One of them is 
the fact, already noted, that common sense is concerned with a 
field that is dominantly qualitative, while science is compelled by 
its own problems and goals to state its subject-matter in terms of 
magnitude and other mathematical relations which are non- 
qualitative. The other fact is that since common sense is con- 
cerned, directly and indirectly, with problems of use and enjoy- 
ment, it is inherently teleological. Science, on the other hand, has 
progressed by elimination of "final causes" from every domain 
with which it is concerned, substituting measured correspondences 
of change. It operates, to use the old terminology, in terms of 
"efficient causation," irrespective of ends and values. Upon the 
basis of the position here taken, these differences are due to the 
fact that different types of problems demand different modes of 
inquiry for their solution, not to any ultimate division in existential 
subject-matter. 

The subject-matter of science is stated in symbol-constellations 
that are radically unlike those familiar to common sense; in what, in 
effect, is a different language. Moreover, there is much highly 
technical material that has not been incorporated into common 
sense even by way of technological application in "material" af- 



COMMON SENSE AND SCIENTIFIC INQUIRY 77 

fairs. In the region of highest importance to common sense, 
namely, that of moral, political, economic ideas and beliefs, and the 
methods of forming and confirming them, science has had even 
less effect. Conceptions and methods in the field of human re- 
lationships are in much the same state as were the beliefs and 
methods of common sense in relation to physical nature before 
the rise of experimental science. These considerations fix the 
meaning of the statement that the difference that now exists be- 
tween common sense and science is a social, rather than a logical, 
matter. If the word "language" is used not just formally, but to 
include its content of substantial meanings, the difference is a 
difference of languages. 

The problems of science demand a set of data and a system of 
meanings and symbols so differentiated that science cannot rightly 
be called "organized common sense." But it is a potential organ 
for organizing common sense in its dealing with its own subject- 
matter and problems and this potentiality is far from actualization. 
In the techniques which affect human use of the materials of 
physical nature in production, science has become a powerful 
agency of organization. As far as issues of enjoyment, of con- 
sumption, are concerned, it has taken little effect. Morals and 
the problems of social control are hardly touched. Beliefs, con- 
ceptions, customs and institutions, whose rise antedated the modern 
period, still have possession of the field. The union of this fact 
with the highly technical and remote language of science creates 
and maintains the feeling and idea of a complete gap. The paths 
of communication between common sense and science are as yet 
largely one-way lanes. Science takes its departure from common 
sense, but the return road into common sense is devious and 
blocked by existing social conditions. 

In the things of greatest import there is little intercommunica- 
tion. Pre-scientific ideas and beliefs in morals and politics are, more- 
over, so deeply ingrained in tradition and habit and institutions, that 
the impact of scientific method is feared as something profoundly 
hostile to mankind's dearest and deepest interests and values. On 
the side of philosophical formulation, highly influential schools of 
thought are devoted to maintaining the domain of values, ideas 
and ideals as something wholly apart from any possibility of ap- 



78 INTRODUCTION: THE MATRIX OF INQUIRY 

plication of scientific methods. Earlier philosophic conceptions of 
the necessary separation between reason and experience, theory 
and practice, higher and lower activities, are used to justify the 
necessity of the division. 

With respect to the second point, that of a seeming funda- 
mental difference due to the fact that common sense is profoundly 
teleological in its controlling ideas and methods while science is 
deliberately indifferent to teleology, it must be noted that in spite 
of the theoretical difference, physical science has, in practical 
fact, liberated and vastly extended the range of ends open to 
common sense and has enormously increased the range and power 
of the means available for attaining them. In ancient thought, 
ends were fixed by nature; departure from those ends that were 
antecedently set and fixed by the very nature of things, was im- 
possible; the attempt to institute ends of human devising was taken 
to be the sure road to confusion and chaos. In the moral field, 
this conception still exists and is even probably dominant. But in 
respect to "material" affairs, it has been completely abandoned. 
Invention of new agencies and instruments create new ends; they 
create new consequences which stir men to form new purposes. 

The original philosophical meaning of "ends" as fixed comple- 
tions is almost forgotten. Instead of science eliminating ends and 
inquiries controlled by teleological considerations, it has, on the 
contrary, enormously freed and expanded activity and thought in 
telic matters. This effect is not a matter of opinion but of facts 
too obvious to be denied. The same sort of thing holds of the 
qualities with which common sense is inextricably concerned. 
Multitudes of new qualities have been brought into existence by 
the applications of physical science, and, what is even more im- 
portant, our power to bring qualities within actual experience 
when we so desire, has been intensified almost beyond the pos- 
sibility of estimate. Consider, as one instance alone, our powers 
with respect to qualities generated by light and electricity. 

The foregoing survey is made for a double purpose. On the 
one hand the outstanding problem of our civilization is set by the 
fact that common sense in its content, its "world" and methods, is 
a house divided against itself. It consists in part, and that part the 
most vital, of regulative meanings and procedures that antedate 



COMMON SENSE AND SCIENTIFIC INQUIRY 79 

the rise of experimental science in its conclusions and methods. In 
another part, it is what it is because of application of science. This 
cleavage marks every phase and aspect of modern life: religious, 
economic, political, legal, and even artistic. 

The existence of this split is put in evidence by those who con- 
demn the "modern" and who hold that the only solution of the 
chaos in civilization is to revert to the intellectual beliefs and 
methods that were authoritative in past ages, as well as by radicals 
and "revolutionaries." Between the two stand the multitude that 
is confused and insecure. It is for this reason that it is here 
affirmed that the basic problem of present culture and associated 
living is that of effecting integration where division now exists. 
The problem cannot be solved apart from a unified logical method 
of attack and procedure. The attainment of unified method means 
that the fundamental unity of the structure of inquiry in common 
sense and science be recognized, their difference being one in the 
problems with which they are directly concerned, not to their re- 
spective logics. It is not urged that attainment of a unified logic, 
a theory of inquiry, will resolve the split in our beliefs and pro- 
cedures. But it is affirmed that it will not be resolved without it. 

On the other hand, the problem of unification is one in and for 
logical theory itself. At the present time logics in vogue do not 
claim for the most part to be logics of inquiry. In the main, we are 
asked to take our choice between the traditional logic, which was 
formulated not only long before the rise of science but when also 
the content and methods of science were in radical opposition to 
those of present science, and the new purely "symbolistic logic" that 
recognizes only mathematics, and even at that is not so much con- 
cerned with methods of mathematics as with linguistic formula- 
tion of its results. The logic of science is not only separated from 
common sense, but the best that can be done is to speak of logic 
afid scientific method as two different and independent matters. 
Logic in being "purified" from all experiential taint has become so 
f ormalistic that it applies only to itself. 

The next chapter deals explicitly with the traditional logic as 
derived from Aristotle, with a view to showing (1) that of neces- 
sity the scientific conditions under which it was formulated are so 
different from those of existing knowledge that it has been trans- 



80 INTRODUCTION: THE MATRIX OF INQUIRY 

formed from what it originally was, a logic of knowledge, into a 
purely formal affair, and (2) that there is a necessity for a logical 
theory based upon scientific conclusions and methods. These are 
so unlike those of classic science that the need is not revision and 
extension of the old logic here and there, but a radically different 
standpoint and a different treatment to be carried through all 
logical subject matter. 



CHAPTER V 

THE NEEDED REFORM OF LOGIC 



■^here are not many today who would echo the saying of 
Kant about logic: "Since Aristotle it has not had to retrace 
. a single step . . . and has not been able to make a single step 
in advance so that, to all appearance, it may be considered as com- 
plete and perfect." Nevertheless the prestige of that logic is still 
enormous. It forms the backbone of most logical texts that are 
taught in the schools, with additional chapters on "inductive logic" 
which are introduced, apparently, out of a feeling of need to pay 
some deference to what are supposed to be the methods of modern 
science. 

Even those who realize the imperfections of classic logic in, for 
example, its assumption of the conception of fixed substances as 
necessary subjects of every proposition, do, nevertheless, pay 
homage even in their formal symbolic statements to traditional 
forms, contenting themselves with revisions and additions here and 
there. Those who, like John Stuart Mill, have systematically 
criticized the traditional theory and who have attempted to build 
a logic in accord with modern scientific practices, have disastrously 
compromised their case by basing their logical constructions 
ultimately upon psychological theories that reduced "experience" 
to mental states and external associations among them, instead of 
upon the actual conduct of scientific inquiry. 

No apology is needed, therefore, for discussion of Aristotelian 
logic in relation to the theory of logic developed in this volume. 
For the former enters so vitally into present theories that considera- 
tion of it, instead of being historical in import, is a consideration of 
the contemporary logical scene. The competency of traditional 
logic as an organ of inquiry into existing problems of common 
sense and science is an urgent question. This chapter is, accord- 

81 



82 INTRODUCTION: THE MATRIX OF INQUIRY 

ingly, a critical exposition of the main features of the Aristotelian 
logic in reference (1) to the conditions of science and culture 
which provided its background and substantial material, and (2) 
to their contrast with the conditions of culture and science which 
now obtain. The first point involves the attempt to show the 
intimate and organized way in which the classic logic reflected 
the science of the period in which it was formulated. The second 
point concerns the revolutionary change that has since taken 
place in science as the ground for a correspondingly radical change 
in logic. 

A recent writer on logic has said: "Science seeks today to 
establish for the most part what are called 'laws of nature'; and 
these are generally answers rather to the question: 'Under what 
conditions does such and such a change take place?' or 'What are 
the most general principles exemplified in such and such a change?' 
than to the question, 'What is the definition of such and such a 
subject?', or 'What are its essential attributes?' It is more in 
respect of the problems to be answered, than of the logical char- 
acter of the reasoning by which we must prove our answers to 
them, that Aristotle's views (as represented in the Topics) are 
antiquated." 1 

The implication of this passage, especially when it is extended to 
apply to logical works other than the Topics, would seem to be 
that a radical change in the problems and objects of inquiry 
(like the change from unchanging substances and their necessary 
essential forms to correlations of change) can take place with little 
change in logical forms. This implicit assumption is characteristic 
of much current logical writing. A contrary postulate is the 
ground for the present examination of Aristotelian logic in its 
relation to Greek science and culture in the fifth century u.c. 
The more adequate that logic was in its own day, the less fitted is 
it to form the framework of present logical theory. 

Greek culture was extraordinarily rich in artistic accomplish- 
ment. It is noted also for acute and varied observations of natural 
phenomena and for comprehensive generalizations of what was 
observed. Medicine, music and astronomy, meteorology, language, 
1 H. W. Joseph, An Introduction to Logic, pp. 387-8. 



THE NEEDED REFORM OF LOGIC 83 

and political institutions were all studied with the means at com- 
mand in ways freer from external control than was the case 
in any previous civilization. Moreover, the special results in 
these varied fields were welded into that single comprehensive 
view which, following the Greek example, has ever since gone by 
the name of philosophy. Especially notable is the fact that, in 
the absence of the later sharp division between "subject" and 
"object," psychology was a science allied to biology which in 
turn was allied to physics, while morals and politics were parts of 
theory of Nature. Man was conceived in relation to nature, not 
as something set apart. Moral and political studies were not 
separated by sharp boundaries from cosmology. Mathematics, 
moreover, was thought to be an existential science. 

Because of these facts, the conception that was entertained of 
Nature as a whole became the finally decisive consideration. One 
does not have to go into controversies that have arisen regarding 
the meaning of the word nature as used by the early scientist- 
philosophers, to be aware that earlier meanings finally bifurcated 
into two significant directions. "Phusis" the word translated as 
"nature" is etymologically connected with a root meaning "to 
grow." Now growth is change; it is coming into Being and 
passing out of Being, altering between the two extremes of birth 
and death. The adjective "physical" was employed by Aristotle 
to designate this aspect of Nature. The physical was not set over 
against the mental and psychical, for these were also "physical" 
in the sense of being marked by change. But, as we speak today of 
the "nature of things," so Nature in its most emphatic and eulogis- 
tic sense consisted of unchanging substances with their fixed es- 
sential characters or "natures." The distinction and relation of the 
permanent, the fixed, from and to the variable and changing, was 
the ultimate problem of science and philosophy. The philosophy 
of Aristotle is a systematic exposition and organized solution of 
this problem carried through all subjects with which inquiry was 
there concerned. 

This basic fact has a fundamental connection with Aristotelian 
logic. On the negative side, this logic was not formal in the 
sense in which forms are independent of existential subject-matter. 
It was formal, but the forms were those of existence in so far as 



84 INTRODUCTION: THE MATRIX OF INQUIRY 

existence is known — known as distinct from being merely sensed, 
or discursively thought about, or an object of guess and opinion. 

That the significance of the words "subject" and "object" has 
undergone reversal in the history of philosophic thought is a well 
known fact. What we call "objects" were in Greek terminology 
subjects; they were existences taken in their status as subject-mmtx 
of knowledge. Their logical forms were determined by the basic 
division supposed to exist in Nature between the changing and 
the eternal. Things that change are too unstable to be subjects 
of knowledge in its exact and complete sense. Knowledge as 
distinct from sense and opinion is fixed; truth does not alter. 
Hence its subjects ("objects" in our sense) must also be in- 
variable. Seen from this point of view, Nature presented the 
scientific mind with an ordered grade or hierarchy of qualitative 
things from emptiness up to Being in its full sense. 

That which truly is cannot change; the existence of change is 
thus proof of lack of complete Being, of what the Greeks some- 
times called, because of emphasis upon lack of substantiality, Non- 
being. The various grades of intellectual apprehension corre- 
sponded, with their logical forms, point for point with the graded 
ranking of subjects in their qualitative degrees of Being. 

Idiomatic speech today often uses the words whole and perfect 
as synonyms in contradistinction to the broken, the partial and 
imperfect. It is not too much to say that the implications of the 
identifications and the distinctions involved were determinative of 
Greek cosmology and theory of Being. Greek culture in its 
characteristic attitudes was definitely esthetic. Works of art are 
qualitative wholes; "pieces" of them are merely physical. The 
Greek urn as well as the Greek statue and temple were works of 
art; complete and, as we still say, finished. Measure, fixed limits, 
fixed ratio and proportions, are the mark of everything that truly is. 

Such objects, or subjects, are substances having design and form 
in an objective sense. Change and susceptibility to variation lack, 
on the other hand, measure. They are marks of the presence of 
the indefinite; the finite, finished and complete are such because of 
fixed limits and measure. Change as such escapes intellectual ap- 
prehension. It can be known only in so far as it can be included 
within fixed boundaries which mark its beginning and its objective 



THE NEEDED REFORM OF LOGIC M 

end or close; that is, as far as change tends to move toward a 
final and unchanging limit. Change, is known, in other words, 
only as it is enclosed within fixed limits. From the side of knowl- 
edge and logical forms, the changing is sensible, particular or 
partial, while the measured whole, defined by limits, is the rational. 
The syllogism is the form of complete enclosure. It is of two 
types; in one, that which is enclosed as well as the limiting and 
enclosing is permanent; in the other, that which is held within 
bounds is itself in process of change or is "physical" not rational 

The first type of syllogism is that of rational knowledge, which 
is knowledge in its complete sense. This syllogistic form is strictly 
necessary and demonstrative in its contents. The other type of 
syllogism expresses contingent knowledge, which has various 
degrees of probability but in no case is necessary, because its 
subject-matter sometimes is and sometimes is not. The relation of 
inclusion is basic in both forms. Inclusion, however, involves ex- 
clusion. That which is fixed and permanent by nature excludes 
every other substance by its very nature. Being just what it is 
by reason of its eternal nature or essence, it is not anything else. 
Thus in addition to the fundamental logical form of universal 
(complete because dealing with what is whole by nature) and 
necessary propositions and relations of propositions, there are 
positive and negative propositions corresponding to ontological 
inclusions and exclusions. 2 

The so-called major and minor propositions respectively set 
forth the including and included "subjects," while the "middle 
term" is the ratio or logos, reason, the principle of measure and 
limit, which is the ground of inclusion or exclusion. It is in- 
dispensable in reasoning not because of any peculiar property of 
"thought" but because of the inherent connections in nature which 
bind "subjects" together and prevent their mingling. Since the 
middle term represents the principle of inclusion and exclusion in 
nature, it expresses a universal or whole. If it represented that 
which is particular (broken and partial) it could not be the ground 
or reason of that omclusion which is the exhibition in knowledge 
of delusions and inclusions in Nature. 

2 The technical scheme of figures of syllogisms and their relations to one 
another follows so directly that the topic will not be taken up. 



S6 INTRODUCTION: THE MATRIX OF INQUIRY 

That which is included or excluded is of necessity of a kind or 
species. For singular objects, a man, a rock, a particular com- 
munity, come into being and pass out of being. They are particu- 
lar (partial), not complete. The species or kind of which the 
singular is a part is eternal. Humanity is a species, and as a 
substantial species it does not originate nor pass away with the birth 
or death of Socrates, Alcibiades, Xenophon, etc. The substantial 
species is necessarily present in every particular or part, making it 
to be what it is, whether man, horse, oak tree or rock. That which 
belongs inherently and necessarily to a species is its nature or 
essence. Definition is the form which essence takes qua known. 
Far from being verbal or even a convenient process or product of 
"thought," definition is cognitive grasp of that which defines 
(marks out) ontological substance. It marks it off from every- 
thing else and grasps its eternal self -same character. 

Species, moreover, form a graded hierarchy. There are "sensible 
species" represented by the qualities wet-dry, hot-cold, heavy- 
light. Here the phase of change, of the physical, is at its maximum. 
These qualities are always transient and always tending to pass into 
their opposites. Nevertheless, while particular existential qualities 
change, their kinds are fixed. Therefore, a lowest kind of cognitive 
apprehension, that of sense, can exist with respect to them. Even 
sense, in order to apprehend a quality, red, hard, must include it in 
its appropriate species — must classify it. At the other extreme, are 
species devoid of matter and change. The objects in which their 
essential nature is embodied, are constant and unswerving in their 
activities and movements. 

The typical Aristotelian instance is that of the fixed stars, each 
of which pursues its eternal round without any variation. Be- 
tween these two types of species come all the other kinds of 
phenomena and objects in the universe. To go into detail about 
them would be to rehearse the physics and cosmology of Aristotle. 
Suffice it to say that each kind is fixed in the order of Nature, and 
hence in degree of scientific or demonstrative knowledge, by the 
relative degree of variation to which it is subject. The latter trait 
marks the extent in which matter, the principle of instability and 
variation, is present. The higher species are marked by regularity 
of movement toward a fixed end or completion. 



THE NEEDED REFORM OF LOGIC 87 

It is to be noted that the activities of living things are marked by 
an unusual degree of regular recurrence. This fact means that 
they are actuated by an unusual degree of self -movement. Their 
energy of self -movement is such that it resists change due to ex- 
ternal circumstance much more than is the case not only with 
sense qualities (which are subject to change from all things about 
them) but also than in the case of such phenomena as weather 
and all inanimate things. This self-moving and self-governing 
trait of living creatures is of special importance because there is a 
qualitative hierarchy among living creatures. At the lower and 
inferior end are plants and their "vegetative functions," which per- 
sist in absorption and assimilation of food. Energy of self -move- 
ment marks also the various species of animal life. 

At the apex is man. He retains both vegetative and animal 
functions; sensation, appetite, and locomotion. But in so far as 
man attains to rationality as such, pure in the sense of freedom 
from need, sensation and sense-perception, the energy of self- 
movement comes to completion. Reason is pure self-moving 
activity, having no dependence upon and no truck with anything 
outside itself. Such pure self-activity defines God and so far as 
mortals attain to it, they put off mortality. 

From this survey, certain main points about the Aristotelian 
logic emerge. In the first place, the forms recognized are not 
formalistic. They are not independent of "subjects" known. On 
the contrary, they are the forms of these subjects as far as the 
latter are actualized in knowledge. In the second place, knowl- 
edge, in its logical forms, consists exclusively of definition and 
classification. Neither of these processes is linguistic, psychologi- 
cal, nor yet an aid in reflection. Definition is grasp of the essence 
which makes things to be what they truly are. Classification con- 
cerns the ontological exclusions and inclusions of real natural 
kinds or species. Definition and taxonomic classification are neces- 
sary forms of knowledge because they are expressions of necessary 
forms of Being. 

In the third place, there is no room for any logic of discovery 
and invention. Discovery was thought of under the head of learn- 
ing, and learning was merely coming into possession of that al- 
ready known — as a pupil comes to know that already known by 



SS INTRODUCTION: THE MATRIX OF INQUIRY 

teacher and textbook. Learning belonged in the inferior region of 
change, and like every mode of change comes to something 
amounts to something, only as it falls within fixed limits of knowl- 
edge. In the case of learning (the sole form of discovery) the 
limits are apprehension of the species present in objects of percep- 
tion on one hand and rational grasp of some essence defining a com- 
plete species or whole on the other hand. Learning merely brings 
these two antecedently given forms of knowledge into connection 
with each other. Similarly, invention of the new had no place. 
It had only its literal etymological meaning of coining upon some- 
thing already there. 

These considerations explain the ease with which a logical 
theory which was strictly ontological or existential in its original 
reference became a merely formal logic when the advance of 
science destroyed the background of essences and species upon 
which the original logic was based. The latter had no place for 
discursive or reflective operations save as processes of personal de- 
velopment (such as might now be called psychological but are 
rather pedagogical) by means of which individual persons arrived 
at direct apprehension of essences and of relations of inclusion and 
exclusion. Hence the perpetuation of the forms of the Aristotelian 
tradition, with elimination of the subject-matter of which they 
were the forms, also ruled out inquiry (which is effective reflec- 
tion) from the proper scope of logic. The syllogism in the origi- 
nal logic was in no way a form of inferring or reasoning. It was 
immediate apprehension or vision of the relations of inclusion and 
exclusion that belong to real wholes in Nature. 

In its final and complete sense all knowledge in the classic scheme 
is immediate rational apprehension, grasp or vision. Reflection and 
inquiry were of the nature of the maneuvering that an individual 
may be forced to engage in so as to get a better view of something 
already there, like making a journey to a museum to inspect the 
objects found in it. Form (eidos) and species are views of wholes. 
Because of the weakness of mortal flesh men have to engage in re- 
flective inquiries, but the latter are of no inherent logical impor- 
tance. Knowledge, when arrived at, is grasp and possession: of 
the nature of "intuition" in modern theory, only having none of 
the vagueness of "intuition" as that word is now used. 



THE NEEDED REFORM OF LOGIC 89 

From our present point of view, Aristotle's saying that things 
of sense are better known in relation to us while rational objects 
are better known in themselves, is at least obscure. If, however, 
the etymological connection between gignoskai, gnoscere and 
know with note is borne in mind, the obscurity vanishes. To 
know was to note, and all that could be truly noted was that which 
already marked the subject of knowledge in Nature. Sensible and 
changing things are themselves noted, not merely notable, in rela- 
tion to us; rational objects are noted and marked off in and of 
themselves, so that knowledge is attainment to vision of existential 
defining marks or objective notations. 3 

I come now to the fundamental difference between the Greek 
conception of Nature as it is expressed in Aristotelian cosmology, 
ontology and logic, and the modern conception as that has been de- 
termined in the scientific revolution. The most evident point of 
difference concerns the entirely different position given to the 
qualitative and the quantitative in their relations to one another. 
It is not merely that classic cosmology and science were consti- 
tuted in terms of qualities, beginning with the four qualitative ele- 
ments, earth, air, fire and water (themselves constituted by 
combinations of the contraries wet-dry, cold-hot, heavy-light) , but 
that all quantitative determinations were relegated to the state of 
accidents, so that apprehension of them had no scientific standing. 
"Accident" is, of course, here a technical term. It does not imply 
that there is no cause for things existing in one amount rather than 
another, but that the cause is so external to the thing in question 
as not to be a ground or reason in knowledge. 

The meaning of "accident" is determined by contrast with es- 
sence. That which is accidental is no part of essence and does 
not follow in any way from essence. Since the latter is the proper 
subject of knowledge, and since quantity (magnitude, amount) is 
wholly irrelevant to essence, consideration of it is outside the scope 
of knowledge in any grade except that of sense. As matter of 
sense it tends, moreover, to prevent ascent above sense to under- 

3 Were epistemological considerations pertinent, attention would have to be 
called to the fact that the classic logic cannot be understood in terms of the 
relation of subject and object, but only in that of the relation of potentiality and 
actuality, where change as potentiality occurs between the limits fixed in 
actuality by Nature. 



90 INTRODUCTION: THE MATRIX OF INQUIRY 

standing. There was, therefore, on the basis of the Aristotelian 
theory of Nature and knowledge no point or purpose in making 
measurements except for lower "practical" ends. Quantity, the 
thing to be measured, fell wholly within the scope of more and 
less, fewer and greater, larger and smaller, or the changing. Meas- 
uring was useful to the artisan in dealing with physical things, but 
that very fact indicated the gulf which separated quantity and 
measuring from science and rationality. Observe by contrast the 
place occupied by measuring in modern knowledge. 1 Is it then 
credible that the logic of Greek knowledge has relevance to the 
logic of modern knowledge? 

Another closely connected difference is found in the fact that 
because of the qualitative nature of the subject-matter of knowl- 
edge in the Greek conception of Nature, heterogeneity was postu- 
lated, as a matter of course, where modern science postulates 
homogeneity, endeavoring to substitute homogeneity for qualita- 
tive diversity. The difference is illustrated in the contrast between 
the present theory of "chemical" elements and the four qualitative 
elements (five, including the etherial substance of the fixed stars). 
The most striking instance, however, is found in the conception 
of qualitatively different kinds of movement that controlled 
science until, say, the sixteenth century. Instead of motion as 
measured change of position in space occupying a measured 
amount of time, circular movement, to and fro, and up and down, 
movements were conceived to be qualitatively exclusive of one 
another. They marked substances of different natures occupying 
places of different values in the hierarchy of species; different ends 
or completions respectively controlled them. Earth comes down 
or falls by its nature and by the nature of its proper place; fire and 
light move up for a similar reason. Levity is as much an inherent 
quality as is gravity, and so with the "essences" of other modes of 
movement. 

Because of the teleological principle that knonjoable change tends 
toward a limiting fixed end, all motion was thought to tend nat- 
urally to come to a state of rest. This notion controlled science 
till, say, the time of Galileo. Note in contrast the place of homo- 

4 Measuring as something we do is radically other than the measure, or relation 
of fixed limits, that controls change. 



THE NEEDED REFORM OF LOGIC 91 

geneous motion in modern science, a homogeneity differentiated 
by angular direction, momentum and velocity, which are all capa- 
ble of measurement. The difference cannot be dismissed as simply 
a difference in the details of subject-matter and without relevance 
for logic. Self-returning qualitative movement is at the heart of 
the classic conception of reason and rational subjects. Its qualita- 
tive difference from other kinds of movement is the criterion by 
which forms of knowledge are graded. In addition, the difference 
of scientific concern with measurement and magnitude is involved. 

A third closely connected difference is found in the fact that 
modern science is concerned with institution of relations, while 
classic logic is based on a theory of nature which treated all rela- 
tions — save that of inclusion and exclusion of species (which was 
not conceived to be a relation) as accidental, in the same sense in 
which quantity is accidental. To be related meant in the Aris- 
totelian scheme to be dependent upon something outside itself. 
But this dependence was not generalized and regarded as forming 
the very structure of a scientific object. On the contrary, it was 
put in sharp opposition to the independence, self-sufficiency and 
self-activity of "subjects" (substances) that are the only objects of 
scientific and demonstrative knowledge. Now to be here and 
then to be somewhere else was dismissed once for all as the sign 
of inferior matter, while in modern science such a change sets the 
problems of scientific inquiry. 

Taking both measurement and relations into account, it is not 
too much to say that what Greek science and logic rejected are 
now the head corner-stone of science — although not yet of the 
theory of logical forms. Contemporary logic has moved far 
enough to criticize the old logic form. To recognition, for 
example, of propositions of the subject (substance) -predicate 
form it has added relational propositions. This is a marked ad- 
vance. But up to a certain point the addition has increased con- 
fusion in logical theory as a whole, since no consistency of theory 
can be attained as long as the theory of antecedent subjects given 
ready-made to predication is retained. 5 

5 Some specific instances of this confusion will be pointed out later. The 
underlying logical point at issue is not the special Aristotelian conception of sub- 
stance, but the idea that any kind of subject, such as "this" or a sense datum, can 
be given ready-made to predication. 



92 INTRODUCTION: THE MATRIX OF INQUIRY 

The next difference to be mentioned is found in the central place 
occupied by ends and teleology in Aristotelian logic. In convert- 
ing that logic into a merely formal logic the teleological factor has 
disappeared. But teleology was so central in classic logic that it 
may be affirmed that with its disappearance, the reason for the 
Aristotelian logic has also vanished. Nothing is left but an empty 
shell; forms without subject-matter. In concluding this phase of 
the discussion I shall refer to the foundation of all the differences 
that have been mentioned — the reversed attitude of science toward 
change. Completion of the cycle of scientific reversal may be con- 
veniently dated from the appearance of Darwin's Origin of Species. 
The very title of the book expresses a revolution in science, for the 
conception of biological species had been a conspicuous mani- 
festation of the assumption of complete immutability. This con- 
ception had been banished before Darwin from every scientific 
subject save botany and zoology. But the latter had remained the 
bulwark of the old logic in scientific subject-matter. 

When eternal essences and species are banished from scientific 
subject-matter, the forms that are appropriate to them have nothing 
left to which they apply; of necessity they are merely formal. 
They remain in historic fact as monuments of a culture and science 
that have disappeared, while in logic they remain as barren formali- 
ties to be formally manipulated. A striking illustration is afforded 
in the change that has taken place in the status of mathematics. In 
Greek logical theory, mathematics was an existential science. The 
discovery that the relation of the hypothenusc of a right-angled 
triangle whose other sides have the value of one is not numerically 
expressible, showed that magnitude and number as such are com- 
pletely "irrational" or illogical. The fact that a ratio remained con- 
stant, no matter what the magnitude of the size and area of the 
triangle, together with the paradoxes of Zeno, helped to produce 
the doctrine of the "accidental" nature of quantity. It led to the 
notion that true number, as distinct from quantity, is geometrical 
in essence. For geometry was based on the conception of limit- 
ing measures, which determined the forms of objects in the sense 
of their configurations. The movement, represented at first in 
Cartesian algebraic geometry, that effected determination of all 
figures by formulae of generalized numerical coordinates was more 



THE NEEDED REFORM OF LOGIC 93 

than a new instrument of scientific analysis and record. It marked 
the beginning of the logical movement by which all mathematical 
propositions became formulae for dealing with possible objects, 
not descriptions of their existing properties — so that they are 
logically non-existential in their content, save when taken to pre- 
scribe operations of experimental observation. 

The entire matter may be summed up by reference to the differ^ 
ent conceptions of Nature that are involved respectively in ancient 
and modern science. In Greek science, Nature was a qualitative, 
a bounded and closed, whole. To know any special subject was 
to know it as a whole in its proper place in the comprehensively 
inclusive whole, Nature. It is not true that ancient science at- 
tempted to deduce knowledge of the included wholes from the 
conception of the final and complete whole. The notion that 
Greek science was deductive in this sense is a profound misappre- 
hension. In the Greek scheme, knowledge consisted in placing 
each relative species, or whole, defined and identified by its own 
essence, in relation to other species within Nature as the final 
whole. The necessity of referring all special kinds and modes of 
knowledge to Nature as a closed whole explains why, in the classic 
conception, there could be no sharp distinction between science 
and philosophy. The subject-matter of modern natural science 
consists of changes formulated in correspondence with one an- 
other. This fact not only gives a radically different status to 
change but it radically affects the conception of Nature. 

The formulation of correlated correspondences becomes more 
and more comprehensive in scope. But no scientist today would 
dream of setting up an all-inclusive formula for the universe as a 
whole. That job has been taken over by certain philosophic 
schools. The change in the conception of Nature is expressed in 
summary form in the idea that the universe is now conceived as 
open and in process while classical Greece thought of it as finite in 
the sense in which finite means finished, complete and perfect. 
The infinite was the indefinite in Greek science, and the indefinite, 
as such, could not be known. 

It would be completely erroneous to regard the foregoing as a 
criticism of the Aristotelian logic in its original formulation in 



96 INTRODUCTION: THE MATRIX OF INQUIRY 

mon sense and the science of his day. The unification was effected 
in a way which is no longer possible. We can no longer take the 
contents and procedures of both common sense and science as in- 
herently fixed, differing only in qualitative grade and rank in a 
qualitatively fixed hierarchy. The fixity of the contents and logi- 
cal forms of both common sense and science in the Aristotelian 
scheme precluded the possibility of the reaction of science back 
into common sense and the possibility of the ever-continuing rise of 
new scientific problems and conceptions out of the material of 
common sense activities and materials. All that science could do 
was to accept what was given and established in common sense 
and formulate it in its relation to the fixed subjects of higher ra- 
tional knowledge. The present need is for a unified logic that 
takes account of a two-way movement between common sense 
and science. 

The common sense culture which was formulated was of a high 
order. As far as free citizens — those who freely shared in the 
culture — were concerned, it was dominated by esthetic and artistic 
categories of harmony, measure, proportion, objective design and 
wholeness. In addition, the leading conceptions of philosophic 
science were but translations into philosophic vocabulary of con- 
ceptions that dominate common sense in every period. ( 1 ) The 
category of substance is the reflection of the conception that things 
exist in stable form in the world — an idea not only familiar to, but 
basic in, all those common sense beliefs that have not been modified 
by the impact of modern science. These things arc designated by 
the common nouns in general use. (2) The category of fixed 
species corresponds to common sense belief in natural kinds, some 
of which are inclusive of others, while some are exclusive. For 
common sense these natural kinds do not permit of transition from 
one to another nor of any overlapping. The evidence for the 
existence of fixed natural kinds and of substantial objects is over- 
whelming from the standpoint of ordinary common sense. (3) 
Common sense ideas, beliefs and judgments in every culture are 
controlled by teleological conceptions, by ends; in modern lan- 
guage, by considerations of value. (4) Common sense thinks of 
the world of things and social relations in terms which, when they 
are reflectively organized, become the doctrine of graded ranks or 



THE NEEDED REFORM OF LOGIC 97 

hierarchies. Distinctions of low and high, inferior and superior, 
base and noble, and all manner of similar qualitative opposites of 
value, are almost the stuff of common sense beliefs which have not 
been transformed by the impact of science. They seem to be 
guaranteed by the obviously perceived structures of both nature 
and human society. 

When I say that the philosophic science, of which logical theory 
was an integral member, organized these and like beliefs and ideas 
of common sense, it is not meant that the former merely mirrored 
the latter. The very idea of reflective organization negates such a 
notion. Not only were implications of which common sense was 
unaware made explicit, but the framework of conceptions was 
vastly extended by investigations of subjects with which common 
sense held no commerce. Above all, the very fact of organization 
involved an ordered arrangement foreign to common sense. Com- 
mon sense, for example, would hardly have entertained the idea that 
the philosopher-scientist was higher in rank as to his objects and 
activities than the general and the statesman; or that the happiness 
of the former was> of a godlike character in comparison with the 
happiness open to others. But none the less there were things 
involved in Athenian culture which, when they were put in or- 
dered arrangement with one another, took the form of this con- 
clusion. 

We are brought back to the conclusions of the last chapter. The 
subject-matter and methods of modern science have no such direct 
affinity with those of common sense as existed when classic science 
and logic were formulated. Science is no longer an organization 
of meanings and modes of action that have their presence in the 
meanings and syntactical structures of ordinary language. Yet 
scientific conclusions and techniques have enormously altered the 
common sense relation of man to nature and to fellow-man. It 
can no longer be believed that they do not profoundly react to 
modify common sense, any more than it can now be supposed 
that they are but an intellectual organization of the latter. 

Science has, however, affected the actual conditions under 
which men live, use, enjoy and suffer much more than (aside from 
material technologies) it has affected their habits of belief and in- 
quiry. Especially is this true about the uses and enjoyments of 



98 INTRODUCTION: THE MATRIX OF INQUIRY 

final concern: religious, moral, legal, economic, political. The de- 
mand for reform of logic is the demand for a unified theory of 
inquiry through which the authentic pattern of experimental and 
operational inquiry of science shall become available for regula- 
tion of the habitual methods by which inquiries in the field of 
common sense are carried on; by which conclusions are reached 
and beliefs are formed and tested. In the next chapter the nature 
of this common pattern forms the theme of discussion. 



Part Two 

THE STRUCTURE OF INQUIRY AND THE 
CONSTRUCTION OF JUDGMENTS 



CHATTER VI 

THE PATTERN OF INQUIRY 



^jhe first chapter set forth the fundamental thesis of this 
volume: Logical forms accrue to subject-matter when the 

, latter is subjected to controlled inquiry. It also set forth 
some of the implications of this thesis for the nature of logical 
theory. The second and third chapters stated the independent 
grounds, biological and cultural, for holding that logic is a theory 
of experiential naturalistic subject-matter. The first of the next two 
chapters developed the theme with reference to the relations of the 
logic of common sense and science, while the second discussed 
Aristotelian logic as the organized formulation of the language of 
Greek life, when that language is regarded as the expression of the 
meanings of Greek culture and of the significance attributed to 
various forms of natural existence. It was held throughout these 
chapters that inquiry, in spite of the diverse subjects to which it ap- 
plies, and the consequent diversity of its special techniques has a 
common structure or pattern: that this common structure is applied 
both in common sense and science, although because of the nature 
of the problems with which they are concerned, the emphasis upon 
the factors involved varies widely in the two modes. We now come 
to the consideration of the common pattern. 

The fact that new formal properties accrue to subject-matter in 
virtue of its subjection to certain types of operation is familiar to 
us in certain fields, even though the idea corresponding to this fact 
is unfamiliar in logic. Two outstanding instances are provided 
by art and law. In music, the dance, painting, sculpture, literature 
and the other fine arts, subject-matters of everyday experience are 
transi ormed by the development of forms which render certain 
products of doing and making objects of fine art. The materials 
of legal regulations are transactions occurring in the ordinary 

101 



102 THE STRUCTURE OF INQUIRY 



activities of human beings and groups of human beings; transac- 
tions of a sort that are engaged in apart from law. As certain 
aspects and phases of these transactions are legally formalized, con- 
ceptions such as misdemeanor, crime, torts, contracts and so on 
arise. These formal conceptions arise out of the ordinary trans- 
actions; they are not imposed upon them from on high or from 
any external and a priori source. But when they are formed they 
are also formative; they regulate the proper conduct of the activi- 
ties out of which they develop. 

All of these formal legal conceptions are operational in nature. 
They formulate and define 'ways of operation on the part of those 
engaged in the transactions into which a number of persons or 
groups enter as "parties," and the ways of operation followed by 
those who have jurisdiction in deciding whether established forms 
have been complied with, together with the existential consequences 
of failure of observation. The forms in question are not fixed and 
eternal. They change, though as a rule too slowly, with changes in 
the habitual transactions in which individuals and groups engage 
and the changes that occur in the consequences of these transac- 
tions. However hypothetical may be the conception that logical 
forms accrue to existential materials in virtue of the control exer- 
cised over inquiries in order that they may fulfil their end, the con- 
ception is descriptive of something that verifiably exists. The de- 
velopment of forms in consequence of operations is an established 
fact in some fields; it is not invented ad hoc in relation to logical 
forms. 

The existence of inquiries is not a matter of doubt. They enter 
into every area of life and into every aspect of every area. In 
everyday living, men examine; they turn things over intellectually; 
they infer and judge as "naturally" as they reap and sow, produce 
and exchange commodities. As a mode of conduct, inquiry is as 
accessible to objective study as are these other modes of behavior. 
Because of the intimate and decisive way in which inquiry and its 
conclusions enter into the management of all affairs of life, no 
study of the latter is adequate save as it is noted how they are af- 
fected by the methods and instruments of inquiry that currently 
obtain. Quite apart, then, from the particular hypothesis about 
logical forms that is put forth, study of the objective facts of in- 



THE PATTERN OF INQUIRY 103 

quiry is a matter of tremendous import, practically and intellec- 
tually. These materials provide the theory of logical forms with 
a subject-matter that is not only objective but is objective in a 
fashion that enables logic to avoid the three mistakes most charac- 
teristic of its history. 

1. In virtue of its concern with objectively observable subject- 
matter by reference to which reflective conclusions can be tried 
and tested, dependence upon subjective and "mentalistic" states 
and processes is eliminated. 

2. The distinctive existence and nature of forms is acknowl- 
edged. Logic is not compelled, as historic "empirical" logic felt 
compelled to do, to reduce logical forms to mere transcripts of the 
empirical materials that antecede the existence of the former. Just 
as art-forms and legal forms are capable of independent discus- 
sion and development, so are logical forms, even though the "in- 
dependence" in question is intermediate, not final and complete. 
As in the case of these other forms, they originate out of experien- 
tial material, and when constituted introduce new ways of oper- 
ating with prior materials, which ways modify the material out of 
which they develop. 

3. Logical theory is liberated from the unobservable, trans- 
cendental and "intuitional." 

When methods and results of inquiry are studied as objective 
data, the distinction that has often been drawn between noting 
and reporting the ways in which men do think, and prescribing 
the ways in which they ought to think, takes on a very different 
interpretation from that usually given. The usual interpretation 
is in terms of the difference between the psychological and the 
logical, the latter consisting of "norms" provided from some source 
wholly outside of and independent of "experience." 

The way in which men do "think" denotes, as it is here inter- 
preted, simply the ways in which men at a given time carry on 
their inquiries. So far as it is used to register a difference from 
the ways in which they ought to think, it denotes a difference like 
that between good and bad farming or good and bad medical prac- 
tice. 1 Men think in ways they should not when they follow meth- 
ods of inquiry that experience of past inquiries shows are not 

1 Cf. pp. 6 and 10 of Introduction. 



104 THE STRUCTURE OF INQUIRY 

competent to reach the intended end of the inquiries in question, 
Everybody knows that today there are in vogue methods of 
farming generally followed in the past which compare very un- 
favorably in their results with those obtained by practices that 
have already been introduced and tested. When an expert tells a 
farmer he should do thus and so, he is not setting up for a bad 
farmer an ideal drawn from the blue. He is instructing him in 
methods that have been tried and that have proved successful in 
procuring results. In a similar way we are able to contrast various 
kinds of inquiry that are in use or that have been used in respect 
to their economy and efficiency in reaching warranted conclusions. 
We know that some methods of inquiry are better than others in 
just the same way in which we know that some methods of sur- 
gery, farming, road-making, navigating or what-not are better than 
others. It does not follow in any of these cases that the "better" 
methods are ideally perfect, or that they are regulative or "norma- 
tive" because of conformity to some absolute form. They are the 
methods which experience up to the present time shows to be the 
best methods available for achieving certain results, while abstrac- 
tion of these methods does supply a (relative) norm or standard 
for further undertakings. 

The search for the pattern of inquiry is, accordingly, not one 
instituted in the dark or at large. It is checked and controlled by 
knowledge of the kinds of inquiry that have and that have not 
worked; methods which, as was pointed out earlier, can be so com- 
pared as to yield reasoned or rational conclusions. For, through 
comparison-contrast, we ascertain how and why certain means and 
agencies have provided warrantably assertible conclusions, while 
others have not and cannot do so in the sense in which "cannot" 
expresses an intrinsic incompatibility between means used and 
consequences attained. 

We may now ask: What is the definition of Inquiry? That is, 
what is the most highly generalized conception of inquiry which 
can be justifiably formulated? The definition that will be ex- 
panded, directly in the present chapter and indirectly in the follow- 
ing chapters, is as follows: Inquiry is the controlled or directed 
transformation of an indeterminate situation into one that is so de- 
terminate in its constituent distinctions and relations as to con- 



THE PATTERN OF INQUIRY 105 

vert the elements of the original situation into a unified whole. 2 
The original indeterminate situation is not only "open" to in- 
quiry, but it is open in the sense that its constituents do not hang 
together. The determinate situation on the other hand, qua out- 
come of inquiry, is a closed and, as it were, finished situation or 
"universe of experience." "Controlled or directed" in the above 
formula refers to the fact that inquiry is competent in any given 
case in the degree in which the operations involved in it actually 
do terminate in the establishment of an objectively unified existen- 
tial situation. In the intermediate course of transition and trans- 
formation of the indeterminate situation, discourse through use of 
symbols is employed as means. In received logical terminology, 
propositions, or terms and the relations between them, are intrinsi- 
cally involved. 

I. The Antecedent Conditions of Inquiry: The Indeterminate 
Situation. Inquiry and questioning, up to a certain point, are 
synonymous terms. We inquire when we question; and we in- 
quire when we seek for whatever will provide an answer to a 
question asked. Thus it is of the very nature of the indeterminate 
situation which evokes inquiry to be questionable; or, in terms of 
actuality instead of potentiality, to be uncertain, unsettled, dis- 
turbed. The peculiar quality of what pervades the given materials, 
constituting them a situation, is not just uncertainty at large; it is a 
unique doubtfulness which makes that situation to be just and only 
the situation it is. It is this unique quality that not only evokes 
the particular inquiry engaged in but that exercises control over 
its special procedures. Otherwise, one procedure in inquiry would 
be as likely to occur and to be effective as any other. Unless a 
situation is uniquely qualified in its very indeterminateness, there is 
a condition of complete panic; response to it takes the form of 
blind and wild overt activities. Stating the matter from the per- 
sonal side, we have "lost our heads." A variety of names serves to 
characterize indeterminate situations. They are disturbed, trou- 
bled, ambiguous, confused, full of conflicting tendencies, obscure, 
etc. 
It is the situation that has these traits. We are doubtful because 

2 The word "situation" is to be understood in the sense already expounded, 
ante, pp. 66-7. 



106 THE STRUCTURE OF INQUIRY _^ 

the situation is inherently doubtful. Personal states of doubt that 
are not evoked by and are not relative to some existential situation 
are pathological; when they are extreme they constitute the mania 
of doubting. Consequently, situations that are disturbed and trou- 
bled, confused or obscure, cannot be straightened out, cleared up 
and put in order, by manipulation of our personal states of mind. 
The attempt to settle them by such manipulations involves what 
psychiatrists call "withdrawal from reality." Such an attempt is 
pathological as far as it goes, and when it goes far it is the source 
of some form of actual insanity. The habit of disposing of the 
doubtful as if it belonged only to us rather than to the existential 
situation in which we are caught and implicated is an inheritance 
from subjectivistic psychology. The biological antecedent condi- 
tions of an unsettled situation are involved in that state of imbal- 
ance in organic-environmental interactions which has already been 
described. 3 Restoration of integration can be effected, in one case 
as in the other, only by operations which actually modify existing 
conditions, not by merely "mental" processes. 

It is, accordingly, a mistake to suppose that a situation is doubt- 
ful only in a "subjective" sense. The notion that in actual exist- 
ence everything is completely determinate has been rendered 
questionable by the progress of physical science itself. Even if it 
had not been, complete determination would not hold of existences 
as an enviromnent. For Nature is an environment only as it is 
involved in interaction with an organism, or self, or whatever 
name be used. 4 

Every such interaction is a temporal process, not a momentary 
cross-sectional occurrence. The situation in which it occurs is in- 
determinate, therefore, with respect to its issue. If we call it con- 
fused, then it is meant that its outcome cannot be anticipated. It 
is called obscure when its course of movement permits of final 
consequences that cannot be clearly made out. It is called con- 
flicting when it tends to evoke discordant responses. Even were 

3 See, ante, pp. 26-7. 

4 Except of course a purely mentalistic name, like consciousness. The alleged 
problem of "interaction ism" versus automatism, parallelism, etc., is a problem (and 
an insoluble one) because of the assumption involved in its statement — the assump- 
tion, namely, that the interaction in question is with something mental instead of 
with biological-cultural human beings. 



THE PATTERN OF INQUIRY 107 

existential conditions unqualifiedly determinate in and of them- 
selves, they are indeterminate in significance: that is, in what they 
import and portend in their interaction with the organism. The 
organic responses that enter into the production of the state of 
affairs that is temporally later and sequential are just as existential 
as are environing conditions. 

The immediate locus of the problem concerns, then, what kind 
of responses the organism shall make. It concerns the interaction 
of organic responses and environing conditions in their movement 
toward an existential issue. It is a commonplace that in any trou- 
bled state of affairs things will come out differently according to 
what is done. The farmer won't get grain unless he plants and 
tills; the general will win or lose the battle according to the way 
he conducts it, and so on. Neither the grain nor the tilling, 
neither the outcome of the battle nor the conduct of it, are "men- 
tal" events. Organic interaction becomes inquiry when existential 
consequences are anticipated; when environing conditions are ex- 
amined with reference to their potentialities; and when responsive 
activities are selected and ordered with reference to actualization 
of some of the potentialities, rather than others, in a final existential 
situation. Resolution of the indeterminate situation is active and 
operational. If the inquiry is adequately directed, the final issue is 
the unified situation that has been mentioned. 

II. Institution of a Problem. The unsettled or indeterminate 
situation might have been called a problematic situation. This 
name would have been, however, proleptic and anticipatory. The 
indeterminate situation becomes problematic in the very process 
of being subjected to inquiry. The indeterminate situation comes 
into existence from existential causes, just as does, say, the organic 
imbalance of hunger. There is nothing intellectual or cognitive in 
the existence of such situations, although they are the necessary 
condition of cognitive operations or inquiry. In themselves they 
are precognitive. The first result of evocation of inquiry is that 
the situation is taken, adjudged, to be problematic. To see that a 
situation requires inquiry is the initial step in inquiry. 5 

5 If by "two- valued logic" is meant a logic that regards "true and false" as the 
sole logical values, then such a logic is necessarily so truncated that clearness and 
consistency in logical doctrine are impossible. Being the matter of a problem is 
a primary logical property. 



108 THE STRUCTURE OF INQUIRY 

Qualification of a situation as problematic does not, however, 
carry inquiry far. It is but an initial step in institution of a prob- 
lem. A problem is not a task to be performed which a person 
puts upon himself or that is placed upon him by others — like a so- 
called arithmetical "problem" in school work. A problem repre- 
sents the partial transformation by inquiry of a problematic situa- 
tion into a determinate situation. It is a familiar and significant 
saying that a problem well put is half-solved. To find out 'what 
the problem and problems are which a problematic situation pre- 
sents to be inquired into, is to be well along in inquiry. To mis- 
take the problem involved is to cause subsequent inquiry to be 
irrelevant or to go astray. Without a problem, there is blind grop- 
ing in the dark. The way in which the problem is conceived de- 
cides what specific suggestions are entertained and which are dis- 
missed; what data are selected and which rejected; it is the criterion 
for relevancy and irrelevancy of hypotheses and conceptual struc- 
tures. On the other hand, to set up a problem that does not grow 
out of an actual situation is to start on a course of dead work, none- 
theless dead because the work is "busy work." Problems that are 
self -set are mere excuses for seeming to do something intellectual, 
something that has the semblance but not the substance of scientific 
activity. 

III. The Determination of a froblem-Solutloii. Statement of a 
problematic situation in terms of a problem has no meaning save 
as the problem instituted has, in the very terms of its statement, 
reference to a possible solution. Just because a problem well 
stated is on its way to solution, the determining of a genuine prob- 
lem is a progressive inquiry; the cases in which a problem and its 
probable solution flash upon an inquirer are cases where much 
prior ingestion and digestion have occurred. If we assume, pre- 
maturely, that the problem involved is definite and clear, subse- 
quent inquiry proceeds on the wrong track. Hence the question 
arises: How is the formation of a genuine problem so controlled 
that further inquiries will move toward a solution? 

The first step in answering this question is to recognize that 
no situation which is completely indeterminate can possibly be 
converted into a problem having definite constituents. The first 
step then is to search out the constituents of a given situation 



THE PATTERN OF INQUIRY 109 

which, as constituents, are settled. When an alarm of fire is 
sounded in a crowded assembly hall, there is much that is inde- 
terminate as regards the activities that may produce a favorable 
issue. One may get out safely or one may be trampled and 
burned. The fire is characterized, however, by some settled traits. 
It is, for example, located somewhere. Then the aisles and exits 
are at fixed places. Since they are settled or determinate in exist- 
ence, the first step in institution of a problem is to settle them in 
observation. There are other factors which, while they are not as 
temporally and spatially fixed, are yet observable constituents; for 
example, the behavior and movements of other members of the 
audience. All of these observed conditions taken together consti- 
tute "the facts of the case." They constitute the terms of the 
problem, because they are conditions that must be reckoned with 
or taken account of in any relevant solution that is proposed. 

A possible relevant solution is then suggested by the determina- 
tion of factual conditions which are secured by observation. The 
possible solution presents itself, therefore, as an idea, just as the 
terms of the problem (which are facts) are instituted by observa- 
tion. Ideas are anticipated consequences (forecasts) of what will 
happen when certain operations are executed under and with 
respect to observed conditions. 6 Observation of facts and suggested 
meanings or ideas arise and develop in correspondence with each 
other. The more the facts of the case come to light in consequence 
of being subjected to observation, the clearer and more pertinent 
become the conceptions of the way the problem constituted by 
these facts is to be dealt with. On the other side, the clearer the 
idea, the more definite, as a truism, become the operations of ob- 
servation and of execution that must be performed in order to re- 
solve the situation. 

An idea is first of all an anticipation of something that may 
happen; it marks a possibility. When it is said, as it sometimes is, 

6 The theory of ideas that has been held in psychology and epistemology 
since the time of Locke's successors is completely irrelevant and obstructive in 
logical theory. For in treating them as copies of perceptions or "impressions," it 
ignores the prospective and anticipatory character that defines being an idea. 
Failure to define ideas functionally, in the reference they have to a solution of a 
problem, is one reason they have been treated as merely "mental." The notion, 
on the other hand, that ideas are fantasies is a derivative. Fantasies arise when the 
function an idea performs is ruled out when it is entertained and developed. 



HO THE STRUCTURE OF INQUIRY 

that science is prediction, the anticipation that constitutes every 
idea an idea is grounded in a set of controlled observations and of 
regulated conceptual ways of interpreting them. Because inquiry 
is a progressive determination of a problem and its possible solu- 
tion, ideas differ in grade according to the stage of inquiry reached. 
At first, save in highly familiar matters, they are vague. They 
occur at first simply as suggestions; suggestions just spring up, 
flash upon us, occur to us. They may then become stimuli to 
direct an overt activity but they have as yet no logical status. 
Every idea originates as a suggestion, but not every suggestion is 
an idea. The suggestion becomes an idea when it is examined 
with reference to its functional fitness; its capacity as a means of 
resolving the given situation. 

This examination takes the form of reasoning, as a result of 
which we are able to appraise better than we were at the outset, 
the pertinency and weight of the meaning now entertained with 
respect to its functional capacity. But the final test of its posses- 
sion of these properties is determined when it actually functions — 
that is, when it is put into operation so as to institute by means of 
observations facts not previously observed, and is then used to 
organize them with other facts into a coherent whole. 

Because suggestions and ideas are of that which is not present in 
given existence, the meanings which they involve must be cm- 
bodied in some symbol. Without some kind of symbol no idea; a 
meaning that is completely disembodied can not be entertained 
or used. Since an existence (which is an existence) is the support 
and vehicle of a meaning and is a symbol instead of a merely physi- 
cal existence only in this respect, embodied meanings or ideas are 
capable of objective survey and development. To "look at an 
idea" is not a mere literary figure of speech. 

"Suggestions" have received scant courtesy in logical theory. 
It is true that when they just "pop into our heads," because of the 
workings of the psycho-physical organism, they arc not logical. 
But they are both the conditions and the primary stuff of logical 
ideas. The traditional empiristic theory reduced them, as has 
already been pointed out, to mental copies of physical things and 
assumed that they were per se identical with ideas. Consequently 
it ignored the function of ideas in directing observation and in 



THE PATTERN OF INQUIRY 111 

ascertaining relevant facts. The rationalistic school, on the other 
hand, saw clearly that "facts'' apart from ideas are trivial, that 
they acquire import and significance only in relation to ideas. 
But at the same time it failed to attend to the operative and func- 
tional nature of the latter. Hence, it treated ideas as equivalent 
to the ultimate structure of "Reality." The Kantian formula that 
apart from each other "perceptions are blind and conceptions 
empty" marks a profound logical insight. The insight, however, 
was radically distorted because perceptual and conceptual contents 
were supposed to originate from different sources and thus re- 
quired a third activity, that of synthetic understanding, to bring 
them together. In logical fact, perceptual and conceptual ma- 
terials are instituted in functional correlativity with each other, 
in such a manner that the former locates and describes the prob- 
lem while the latter represents a possible method of solution. 
Both are determinations in and by inquiry of the original prob- 
lematic situation whose pervasive quality controls their institution 
and their contents. Both are finally checked by their capacity to 
work together to introduce a resolved unified situation. As dis- 
tinctions they represent logical divisions of labor. 

IV. Reasoning. The necessity of developing the meaning- 
contents of ideas in their relations to one another has been inci- 
dentally noted. This process, operating with symbols (consti- 
tuting propositions) is reasoning in the sense of ratiocination or 
rational discourse. 7 When a suggested meaning is immediately 
accepted, inquiry is cut short. Hence the conclusion reached is 
not grounded, even if it happens to be correct. The check upon 
immediate acceptance is the examination of the meaning as a 
meaning. This examination consists in noting what the meaning 
in question implies in relation to other meanings in the system of 
which it is a member, the formulated relation constituting a propo- 
sition. If such and such a relation of meanings is accepted, then 
we are committed to such and such other relations of meanings 
because of their membership in the same system. Through a se- 
ries of intermediate meanings, a meaning is finally reached which 

7 "Reasoning" is sometimes used to designate inference as well as ratiocination. 
When so used in logic the tendency is to identify inference and implication and 
thereby seriously to confuse logical theory. 



H2 THE STRUCTURE OF INQUIRY 

is more clearly relevant to the problem in hand than the originally 
suggested idea. It indicates operations which can be performed to 
test its applicability, whereas the original idea is usually too vague 
to determine crucial operations. In other words, the idea or mean- 
ing when developed in discourse directs the activities which, when 
executed, provide needed evidential material. 

The point made can be most readily appreciated in connection 
with scientific reasoning. An hypothesis, once suggested and en- 
tertained, is developed in relation to other conceptual structures 
until it receives a form in which it can instigate and direct an 
experiment that will disclose precisely those conditions which 
have the maximum possible force in determining whether the 
hypothesis should be accepted or rejected. Or it may be that 
the experiment will indicate what modifications are required in 
the hypothesis so that it may be applicable, i.e., suited to interpret 
and organize the facts of the case. In many familiar situations, 
the meaning that is most relevant has been settled because of the 
eventuations of experiments in prior cases so that it is applicable 
almost immediately upon its occurrence. But, indirectly, if not 
directly, an idea or suggestion that is not developed in terms of 
the constellation of meanings to which it belongs can lead only 
to overt response. Since the latter terminates inquiry, there is then 
no adequate inquiry into the meaning that is used to settle the 
given situation, and the conclusion is in so far logically un- 
grounded. 

V. The Operational Character of Facts-Meanings. It was 
stated that the observed facts of the case and the ideational con- 
tents expressed in ideas are related to each other, as, respectively, 
a clarification of the problem involved and the proposal of some 
possible solution; that they are, accordingly, functional divisions 
in the work of inquiry. Observed facts in their office of locating 
and describing the problem are existential; ideational subject- 
matter is non-existential. How, then, do they cooperate with 
each other in the resolution of an existential situation? The prob- 
lem is insoluble save as it is recognized that both observed facts 
and entertained ideas are operational. Ideas are operational in 
that they instigate and direct further operations of observation; 
they are proposals and plans for acting upon existing conditions 



THE PATTERN OF INQUIRY IB 

to bring new facts to light and to organize all the selected facts 
into a coherent whole. 

What is meant by calling facts operational? Upon the negative 
side what is meant is that they are not self-sufficient and complete 
in themselves. They are selected and described, as we have seen, 
for a purpose, namely statement of the problem involved in such 
a way that its material both indicates a meaning relevant to resolu- 
tion of the difficulty and serves to test its worth and validity. In 
regulated inquiry facts are selected and arranged with the express 
intent of fulfilling this office. They are not merely results of 
operations of observation which are executed with the aid of 
bodily organs and auxiliary instruments of art, but they are the 
particular facts and kinds of facts that will link up with one an- 
other in the definite ways that are required to produce a definite 
end. Those not found to connect with others in furtherance of 
this end are dropped and others are sought for. Being functional, 
they are necessarily operational. Their function is to serve as 
evidence and their evidential quality is judged on the basis of their 
capacity to form an ordered whole in response to operations pre- 
scribed by the ideas they occasion and support. If "the facts of 
the case" were final and complete in themselves, if they did not 
have a special operative force in resolution of the problematic 
situation, they could not serve as evidence. 

The operative force of facts is apparent when we consider that 
no fact in isolation has evidential potency. Facts are evidential 
and are tests of an idea in so far as they are capable of being or- 
ganized with one another. The organization can be achieved only 
as they interact with one another. When the problematic situa- 
tion is such as to require extensive inquiries to effect its resolution, 
a series of interactions intervenes. Some observed facts point to 
an idea that stands for a possible solution. This idea evokes more 
observations. Some of the newly observed facts link up with 
those previously observed and are such as to rule out other ob- 
served things with respect to their evidential function. The new 
order of facts suggests a modified idea (or hypothesis) which 
occasions new observations whose result again determines a new 
order of facts, and so on until the existing order is both unified 
and complete. In the course of this serial process, the ideas that 



114 THE STRUCTURE OF INQUIRY 

represent possible solutions are tested or "proved." 

Meantime, the orders of fact, which present themselves in con- 
sequence of the experimental observations the ideas call out and 
direct, are trial facts. They are provisional They are "facts" 
if they are observed by sound organs and techniques. But they 
are not on that account the facts of the case. They are tested or 
"proved" with respect to their evidential function just as much as 
ideas (hypotheses) are tested with reference to their power to 
exercise the function of resolution. The operative force of both 
ideas and facts is thus practically recognized in the degree in 
which they are connected with expeiivicm. Naming them "op- 
erational" is but a theoretical recognition of what is involved 
when inquiry satisfies the conditions imposed by the necessity 
for experiment. 

I recur, in this connection, to what has been said about the ne- 
cessity for symbols in inquiry. It is obvious, on the face of mat- 
ters, that a possible mode of solution must be earned in symbolic 
form since it is a possibility, not an assured piescnr existence. 
Observed facts, on the other hand, are existentially present. It 
might seem therefore, that symbols arc not required for referring 
to them. But if they are not carried and treated by means of 
symbols, they lose their provisional character, and in losing this 
character they are categorically asserted and inquiry comes to an 
end. The carrying on of inquiry requires that the facts be taken 
as representative and not just as presented. This demand is met 
by formulating them in propositions — that is, by means of sym- 
bols. Unless they are so represented they relapse into the total 
qualitative situation. 

VI. Common Sense and Scientific Inquiry. The discussion up 
to this point has proceeded in general terms which recognizes no 
distinction between common sense and scientific inquiry. We 
have now reached a point where the community of partem in these 
two distinctive modes of inquiry should receive explicit attention. 
It was said in earlier chapters that the difference between them 
resides in their respective subject-matters, not in their basic logical 
forms and relations; that the difference in subject-matters is due 
to the difference in the problems respectively involved; and, fi- 
nally, that this difference sets up a difference in the ends or ob- 



THE PATTERN OF INQUIRY 115 

jective consequences they are concerned to achieve. Because 
common sense problems and inquiries have to do with the inter- 
actions into which living creatures enter in connection with en- 
vironing conditions in order to establish objects of use and 
enjoyment, the symbols employed are those which have been 
determined in the habitual culture of a group. They form a 
system but the system is practical rather than intellectual. It is 
constituted by the traditions, occupations, techniques, interests, 
and established institutions of the group. The meanings that 
compose it are carried in the common everyday language of com- 
munication between members of the group. The meanings in- 
volved in this common language system determine what individuals 
of the group may and may not do in relation to physical objects 
and in relations to one another. They regulate what can be used 
and enjoyed and how use and enjoyment shall occur. 

Because the symbol-meaning systems involved are connected 
directly with cultural life-activities and are related to each other 
in virtue of this connection, the specific meanings which are pres- 
ent have reference to the specific and limited environing condi- 
tions under which the group lives. Only those things of the 
environment that are taken, according to custom and tradition, 
as having connection with and bearing upon this life, enter into 
the meaning system. There is no such thing as disinterested in- 
tellectual concern with either physical or social matters. For, 
until the rise of science, there were no problems of common sense 
that called for such inquiry. Disinterestedness existed practically 
in the demand that group interests and concerns be put above 
private needs and interests. But there was no intellectual disinter- 
estedness beyond the activities, interests and concerns of the 
group. In other words, there was no science as such, although, as 
was earlier pointed out, there did exist information and techniques 
which were available for the purposes of scientific inquiry and 
out of which the latter subsequently grew. 

In scientific inquiry, then, meanings are related to one another 
on the ground of their character as meanings, freed from direct 
reference to the concerns of a limited group. Their intellectual 
abstractness is a product of this liberation, just as the "concrete" 
is practically identified by directness of connection with environ- 



116 THE STRUCTURE OF INQUIRY 

mental interactions. Consequently a new language, a new system 
of symbols related together on a new basis, conies into existence, 
and in this new language semantic coherence, as such, is the con- 
trolling consideration. To repeat what has already been said, con- 
nection with problems of use and enjoyment is the source of the 
dominant role of qualities, sensible and moral, and of ends in 
common sense. 

In science, since meanings are determined on the ground of 
their relation as meanings to one another, relations become the 
objects of inquiry and qualities are relegated to a secondary status, 
playing a part only as far as they assist in institution of relations. 
They are subordinate because they have an instrumental office, 
instead of being themselves, as in prescientific common sense, the 
matters of final importance. The enduring hold of common sense 
is testified to historically by the long time it took before it was 
sttn that scientific objects are strictly relational. First tertiary 
qualities were eliminated; it was recognized that moral qualities 
are not agencies in determining the structure of nature. Then 
secondary qualities, the wet-dry, hot-cold, light-heavy, which were 
the explanatory principles of physical phenomena in Greek science, 
were ejected. But so-called primary qualities took their place, as 
with Newton and the Lockeian formulation of Newtonian ex- 
istential postulates. It was not until the threshold of our time 
was reached that scientific inquiries perceived that their own 
problems and methods required an. interpretation of "primary 
qualities" in terms of relations, such as position, motion and 
temporal span. In the structure of distinctively scientific objects 
these relations are indifferent to qualities. 

The foregoing is intended to indicate that the different objec- 
tives of common sense and of scientific inquiry demand different 
subject-matters and that this difference in subject-matters is not 
incompatible with the existence of a common pattern in both 
types. There are, of course, secondary logical forms which re- 
flect the distinction of properties involved in the change from 
qualitative and teleological subject-matter to non-qualitative and 
non-teleological relations. But they occur and operate within 
the described community of pattern. They are explicable, and 
explicable only, on the ground of the distinctive problems gen- 



THE PATTERN OF INQUIRY 117 

erated by scientific subject-matter. The independence of scien- 
tific objects from limited and fairly direct reference to the en- 
vironment as a factor in activities of use and enjoyment, is 
equivalent, as has already been intimated, to their abstract char- 
acter. It is also equivalent to their general character in the sense 
in which the generalizations of science are different from the 
generalizations with which common sense is familiar. The gen- 
erality of all scientific subject-matter as such means that it is 
freed from restriction to conditions which present themselves 
at particular times and places. Their reference is to any set of 
time and place conditions — a statement which is not to be confused 
with the doctrine that they have no reference to actual existential 
occasions. Reference to time-place of existence is necessarily in- 
volved, but it is reference to whatever set of existences fulfils the 
general relations laid down in and by the constitution of the 
scientific object. 8 

Summary. Since a number of points have been discussed, it 
will be well to round up conclusions reached about them in a 
summary statement of the structure of the common pattern of 
inquiry. Inquiry is the directed or controlled transformation of an 
indeterminate situation into a determinately unified one. The 
transition is achieved by means of operations of two kinds which 
are in functional correspondence with each other. One kind of 
operations deals with ideational or conceptual subject-matter. 
This subject-matter stands for possible ways and ends of resolu- 
tion. It anticipates a solution, and is marked off from fancy be- 
cause, or, in so far as, it becomes operative in instigation and di- 
rection of new observations yielding new factual material. The 
other kind of operations is made up of activities involving the 
techniques and organs of observation. Since these operations are 
existential they modify the prior existential situation, bring into 
high relief conditions previously obscure, and relegate to the 
background other aspects that were at the outset conspicuous. 

8 The consequences that follow are directly related to the statement in Ch. IV 
that the elimination of qualities and ends is intermediate; that, in fact, the con- 
struction of purely relational objects has enormously liberated and expanded 
common sense uses and enjoyments by conferring control over production of 
qualities, by enabling new ends to be realistically instituted, and by providing 
competent means for achieving them. 



118 THE STRUCTURE OF INQUIRY 

The ground and criterion of the execution of this work of em- 
phasis, selection and arrangement is to delimit the problem in 
such a way that existential material may be provided with which 
to test the ideas that represent possible modes of solution. Sym- 
bols, defining terms and propositions, are necessarily required in 
order to retain and carry forward both ideational and existential 
subject-matters in order that they may serve their proper func- 
tions in the control of inquiry. Otherwise the problem is taken 
to be closed and inquiry ceases. 

One fundamentally important phase of the transformation of 
the situation which constitutes inquiry is central in the treat- 
ment of judgment and its functions- The transformation is ex- 
istential and hence temporal. The pre-cognitive unsettled situa- 
tion can be settled only by modification of its constituents. Ex- 
perimental operations change existing conditions. Reasoning, 
as such, can provide means for effecting the change of conditions 
but by itself cannot effect it. Only execution of existential opera- 
tions directed by an idea in which ratiocination terminates can 
bring about the re-ordering of environing conditions required 
to produce a settled and unified situation. Since this principle also 
applies to the meanings that are elaborated in science, the experi- 
mental production and re-arrangement of physical conditions 
involved in natural science is further evidence of the unity of the 
pattern of inquiry. The temporal quality of inquiry means, 
then, something quite other than that the process of inquiry takes 
time. It means that the objective subject-matter of inquiry under- 
goes temporal modification. 

Terminological. Were it not that knowledge is related to in- 
quiry as a product to the operations by which it is produced, no dis- 
tinctions requiring special differentiating designations would exist. 
Material would merely be a matter of knowledge or of ignorance 
and error; that would be all that could be said. The content of 
any given proposition would have the values "true" and "false" 
as final and exclusive attributes. But if knowledge is related to 
inquiry as its warrantable assertible product, and if inquiry is 
progressive and temporal, then the material inquired into reveals 
distinctive properties which need to be designated by distinctive 
names. As undergoing inquiry, the material has a different logical 



THE PATTERN OF INQUIRY H9 

import from that which it has as the outcome of inquiry. In its 
first capacity and status, it will be called by the general name 
subject-matter. When it is necessary to refer to subject-matter 
in the context of either observation or ideation, the name content 
will be used, and, particularly on account of its representative 
character, content of propositions. 

The name objects will be reserved for subject-matter so far as 
it has been produced and ordered in settled form by means of 
inquiry; proleptically, objects are the objectives of inquiry. The 
apparent ambiguity of using "objects" for this purpose (since the 
word is regularly applied to things that are observed or thought 
of) is only apparent. For things exist as objects for us only as 
they have been previously determined as outcomes of inquiries. 
When used in carrying on new inquiries in new problematic situa- 
tions, they are known as objects in virtue of prior inquiries which 
warrant their assertibility. In the new situation, they are means 
of attaining knowledge of something else. In the strict sense, they 
are part of the contents of inquiry as the word content was de- 
fined above. But retrospectively (that is, as products of prior de- 
termination in inquiry) they are objects. 



CHAPTER VII 

THE CONSTRUCTION OF JUDGMENT 1 



"n terms of the ideas set forth in the last chapter, judgment 
may be identified as the settled outcome of inquiry. It is 

. concerned with the concluding objects that emerge from in- 
quiry in their status of being conclusive. Judgment in this sense is 
distinguished from propositions. The content of the latter is inter- 
mediate and representative and is carried by symbols; while judg- 
ment, as finally made, has direct existential import. The terms af- 
firmation and assertion are employed in current speech inter- 
changeably. But there is a difference, which should have linguistic 
recognition, between the logical status of intermediate subject- 
matters that are taken for use in connection with what they may 
lead to as means, and subject-matter which has been prepared to be 
final. I shall use assertion to designate the latter logical status and 
affirmation to name the former. Even from the standpoint of ordi- 
nary speech, assertio?i has a quality of insistence that is lacking in 
the connotation of the "word "affirmation." We can usually substi- 
tute the phrase "it is held" or "it is said" for u it is affirmed" How- 
ever, the important matter is not the words, but the logical 
properties that are characteristic of different subject-matters. 

A literal instance of judgment in the sense defined is provided 
by the judgment of a court of law in settling some issue which, 
up to that point, has been in controversy. 1. The occurrence of 
a trial-at-law is equivalent to the occurrence of a problematic 
situation which requires settlement. There is uncertainty and 
dispute about what shall be done because there is conflict about 
the significance of what has taken place, even if there is agree- 
ment about what has taken place as a matter of fact — which, of 
course, is not always the case. The judicial settlement is a settle- 

x The word "construction" is here used to cover the operation of construction 
and the structure which results. 

120 



THE CONSTRUCTION OF JUDGMENT 121 

ment of an issue because it decides existential conditions in their 
bearing upon further activities: the essence of the significance of 
any state of facts. 

2. This settlement or judgment is the outcome of inquiry con- 
ducted in the court-hearings. The inquiry exemplifies the pattern 
described in the last chapter. On the one hand, propositions are 
advanced about the state of facts involved. Witnesses testify to 
what they have heard and seen; written records are offered, etc. 
This subject-matter is capable of direct observation and has 
existential reference. As each party to the discussion produces 
its evidential material, the latter is intended to point to a deter- 
minate decision as a resolution of the as yet undetermined situation. 
The decision takes effect in a definite existential reconstruction. 
On the other hand, there are propositions about conceptual subject- 
matter; rules of law are adduced to determine the admissibility 
(relevancy) and the weight of facts offered as evidence. The 
significa?2ce of factual material is fixed by the rules of the existing 
juridical system; it is not carried by the facts independent of the 
conceptual structure which interprets them. And yet, the quality 
of the problematic situation determines which rules of the total 
system are selected. They are different in civil and criminal cases; 
in cases of trespass and of breach of contract. Conceptions have 
been organized in the past under definite rubrics which summarize 
the kinds of interpreting principles that past experience has shown 
to be applicable in the variety of special cases that normally arise. 
The theoretical ideal sought to guide judicial deliberation is a net- 
work of relations and procedures which express the closest possible 
correspondence between facts and the legal meanings that give 
them their significance: that is, settle the consequences which, in 
the existing social system, flow from them. 

3. The final judgment arrived at is a settiement. The case is 
disposed of; the disposition takes effect in existential consequences. 
The sentence or proposition is not an end in itself but a decisive 
directive of future activities. The consequences of these activities 
bring about an existential determination of the prior situation 
which was indeterminate as to its issue. A man is set free, sent 
to prison, pays a fine, or has to execute an agreement or pay 
damages to an injured party. It is this resulting state of actual 
affairs — this changed situation — that is the matter of the final 



122 THE STRUCTURE OF INQUIRY 

settlement or judgment. The sentence itself is a proposition, 
differing, however, from the propositions formed during the trial, 
whether they concern matters of fact or legal conceptions, in 
that it takes overt effect in operations which construct a new 
qualitative situation. While prior propositions are means of in- 
stituting the sentence, the sentence is terminal as a means of insti- 
tuting a definite existential situation. 

Judgment figures, however, in determination of the intermediate 
propositions. When it is ruled that certain evidence is admissible 
and that certain rules of law (conceptual material) arc applicable 
rather than others, something is settled. It is through a series of 
such intervening settlements that the final settlement is constructed. 
Judgment as final settlement is dependent upon a series of partial 
settlements. The judgments by which propositions are deter- 
mined is recognized and marked off linguistically by such words 
as estimates, appraisals, evaluations. In resolution of problems 
that are of a looser quality than legal cases we call them opinions 
to distinguish them from a warranted judgment or assertion. But 
if the opinion held is grounded it is itself the product of inquiry 
and in so far is a judgment. 2 Estimates and appraisals are pro- 
visional; they are means, not ends. Even a judgment of appraisal 
by judges on the bench may be reversed in a higher court, while 
in freer conduct of scientific inquiry such judgments arc expressly 
made subject to modification. The consequences they produce 
in the conduct of further inquiry is the criterion of their value. 
Judgments which intervene are ad- judgments. 

I. Final Judgment is Individual. This caption is elliptical. It 
means that the subject-matter (objects) of final judgment is a 
situation in the sense in which the meaning of that word has been 
explained; it is a qualitative existential whole which is unique. 
"Individual" as here used has nothing to do with simplicity of 
constituents. On the contrary, every situation, when it is ana- 
lyzed, is extensive containing within itself diverse distinctions and 
relations which, in spite of their diversity, form a unified qualita- 
tive whole. What is designated by the word individual has, ac- 
cordingly, to be distinguished from that which is designated by 

2 Opinion in common speech often means a belief entertained without examina- 
tion, being generated by custom, tradition or desire. 



THE CONSTRUCTION OF JUDGMENT 123 

the word singular. Singulars are named by demonstratives, such 
as this, that, here, noiv, or in some cases by proper nouns. The 
difference between a singular and an individual is the same as 
that previously pointed out between an object (or set of objects 
in their severalty) and a situation. 3 Singular objects exist and 
singular events occur within a field or situation. This or that star, 
man, rock or whatever, is always a discrimination or selection 
made for a purpose, or for the sake of some objective consequence 
within an inclusive field. The singular has no import save as a 
term of differentiation and contrast. If its object is taken to be 
complete in itself, loss of differential force destroys all power of 
reference on the part of the demonstrative act. The very ex- 
istence of differentiation, on the other hand, shows that the sin- 
gular exists within an extensive field. 

It follows that determination of a singular is also instrumental 
in determination of a situation which is itself not complete and 
self-sufficient. It is a means of identifying a situation in reference 
to the problem set to inquiry. It represents, at a given stage of 
inquiry, that which is crucial, critical, differentiatingly significant. 
An artisan in carrying on his work at any given time takes note of 
certain aspects and phases of the situation in which his activities 
are involved. He notes just that object or occurrence which is 
decisive in the stage of development arrived at in the whole 
situation which is determinative of what is to be next. The ob- 
jects which are this and that, to which his inquiry and activity are 
immediately directed, are, therefore, constantly changing. As 
one phase of the problem offered by his work is resolved, another 
phase, presented by a new object or occurrence, takes its place. 
Were not the sequence determined by an inclusive situation, whose 
qualitative nature pervades and holds together each successive 
step, activity would be a meaningless hop-skip- jump affair. Ob- 
jects observed and dealt with would be a shifting panorama of 
sudden disconnected appearances and disappearances. Exactly 
the same account may be given of the succession of observations 
which deal with singular objects and occurrences in scientific in- 
quiry. The singular is that upon which inquiry into an individual 
situation pivots under the special conditions that at a given time 

3 Ante, pp. 66-7. 



124 THE STRUCTURE OF INQUIRY 



fix the problem with respect to the conditions to be dealt with 
forthwith. 

The discriminative or differential aspect of the demonstrative 
act and its singular object is suggested in ordinary speech by the 
expression "pointing out." It is impossible merely to point at 
something. 4 For anything or everything in the line of vision or 
gesture may be equally pointed at. The act of pointing is wholly 
indeterminate as to its object. It is not selective within a situation, 
because it is not controlled by the problem which the situation 
sets and the necessity for determining the conditions which then 
and there point to the way in which it shall be resolved. 

The point just made has its logical meaning in disclosure of the 
ambiguity of the word given as that is currently employed in 
logical texts. That which is "given" in the strict sense of the 
word "given," is the total field or situation. The given in the 
sense of the singular, whether object or quality, is the special 
aspect, phase or constituent of the existcntiatly present situation 
that is selected to locate and identify its problematic features with 
reference to the inquiry then and there to be executed. In the strict 
sense, it is taken rather than given. This fact decides the logical 
status of data. They are not isolated, complete or self-sufficient. 
To be a datum is to have a special function in control of the 
subject-matter of inquiry. It embodies a fixation of the problem in 
a way which indicates a possible solution. It also helps to provide 
evidence which tests the solution that is hypothctically enter- 
tained. This theme will be developed in the discussion that follows 
of "thought," that is, inquiry. 

II. The Subject of Judgment. What was said in the last chap- 
ter concerning the pattern of inquiry enables us to identify the 
structure of judgment as conjugate distinction and relation of 
subject-predicate. Observed facts of the case in their dual func- 
tion of bringing the problem to light and of providing evidential 
material with respect to its solution constitute what has tradition- 
ally been called the subject. The conceptual contents which 
anticipate a possible solution and which direct observational opera- 
tions constitute what has traditionally been called the predicate. 

4 Cf. the conditions and results of the pointing reported in the incident de- 
scribed on p. 53. 



THE CONSTRUCTION OF JUDGMENT 125 

Their functional and operative correspondence with each other 
constitutes the copula. 

In this section, I shall consider the subject of judgment. The 
bearing of the conclusions reached up to this point may be fo- 
calized by contrasting them with a doctrine current in logical 
theory. This latter view holds that the existential matter, which 
has ultimately the form of this object or this quality, is given or 
presented in a literal sense to judgment. Judgment proper is then 
confined to the work of predicating something of it, of character- 
izing what is handed out ready-made either to sense-perception 
or to judgment. I select one statement as typical: "In every 
proposition we are determining in thought the character of an 
object present to thought." 5 The contrasting position here taken 
holds that the subject-matters of subject and predicate are de- 
termined in correspondence with each other in and by the process 
of "thought," that is, inquiry. 

Examination of the two opposed theories will start from the 
negative side. We begin by pointing out the difficulties, amount- 
ing to impossibilities, in the customary view advanced in many 
standard treatises. (1) It leaves judgment, as predication, and 
just at the point where its existential material is concerned, en- 
tirely at the mercy of the accidental flux of objects which happen 
to present themselves. It thereby destroys the possibility of 
sequential continuity in "thought." Predication would at one 
moment be characterizing one object, and at the next moment 
some other object, according as changes and shifts in environ- 
ing conditions took place. The occurrence of successive "given" 
or "presented" singulars would be wholly determined by condi- 
tions outside of inquiry and therefore accidental and irrelevant. 
(2) The view would be another version of the old doctrine of 
passive receptivities, were it not that some active response is de- 
manded in order to institute something to which a demonstrative 
term may be applied. Even then, there is nothing to ground the 
act of pointing so as to select one "this" rather than another. (3) 
Nor is there anything in a mere given "this" to ground one char- 
acterizing predicate rather than another. Either "this" is so 
empty that nothing can be said of it except "this is this" where 

" W. E. Johnson, Logic, Part I, pages 9 and 11. 



126 THE STRUCTURE OF INQUIRY 

"this" signifies nothing beyond the mere presence of an indefinite 
somewhat, or else any one of a large number of predications can 
equally well be made. The truth is that the view criticized can be 
intelligibly stated only after inquiry has already made out some fact 
or set of facts and when the emphatic problem has become that of 
knowing how it should be characterized. The view owes whatever 
plausibility it appears to have to the fact that it begins its account 
of judgment after inquiry has been operative and has already 
established a partial judgment or appraisal. As was indicated in 
the prior chapter, in situations whose recognized constituents are 
similar to those of prior experiences, certain objects are likely to 
stand out sufficiently so as to afford clews. But (a) they do so as 
products of prior judgments, and (b) in any case they are pro- 
visional as evidential data. For they may be misleading clews be- 
cause they turn out to be not "the facts of the case," or what is 
significant in respect to the present problem. 

Suppose that in a given case, this is characterized "Washington 
Monument/' The act of pointing does not determine any one 
"this" rather than another since everything in the line of pointing 
is pointed at. In the second place, even when we suppose that 
the act of pointing happens to land, so to speak, upon one singular 
rather than another, it is only a group of sensible qualities that is 
indicated. There is nothing in these qualities, apart from the con- 
trol of their interpretation by an inclusive situation, to justify 
characterizing them as the Washington Monument — or as a me- 
morial of any kind. The most that could be said is that the 
qualities observed in consequence of the demonstrative act are 
just the qualities they are. The nub of any existential identifica- 
tion or characterization of a thing as such-and-such lies in the 
ground it offers for giving the object a description in terms of 
what is not then and there observed. Apart from an inclusive 
situation which determines in correspondence with each other the 
material that constitutes the observed singular this and the kind 
of characterizing predicate applicable to it, predication is to- 
tally arbitrary or ungrounded. There must be some one question 
to which both the subject "this" and the predicate (say, Washing- 
ton Monument) are relevant. That question grows out of and is 
controlled by some total situation. Otherwise propositions made 
are pointless. 



THE CONSTRUCTION OF JUDGMENT 111 

Any proposition in which "this" appears is then instituted by a 
judgment of appraisal in which "this" is determined in order to 
provide evidential grounds for the qualification attached to it by 
the predicate. This fact is inconsistent with "this" being a mere 
this. There is, however, no incompatibility between the fact that 
it is just what it existentially is and the estimate that it is the needed 
evidential ground of a definite characterization. Stating the 
matter positively, the operations that institute a "this" as subject 
are always selective-restrictive of something from out of a larger 
field. What is selected and what is rejected flows from an estimate 
of their probable evidential significance. 

III. Subjects and Substances. According to the original Aris- 
totelian logic, certain objects, such as species, are logical subjects 
by Nature, since they are substances in Nature, so that only propo- 
sitions having substances for their subjects can enter into rationally 
demonstrative knowledge or science. This theory of the nature 
of the logical subject at least recognizes that the logical subject 
has a determinate nature capable of grounding what is predicated 
of it. But the progress of science has destroyed the idea that 
objects as such are eternal substances, even such objects as the 
"fixed stars." 6 It also destroyed the notion of immutable kinds 
marked off from one another by fixed essences. The following 
problem accordingly arises: If the logical subject cannot be iden- 
tified either with an object or sense-datum directly given to judg- 
ment for qualification through predication, nor yet with an 
ontological "substance," what is meant by being an object sub- 
stantial in any sense that makes it capable of serving as a subject? 

The answer to this question is implicit in what has been said. 
The subject is existential, either a singular this, or a set of singulars. 
But there are conditions of inquiry which must be satisfied by 
anything taken to be a subject. (1) It must delimit and describe 
the problem in such a way as to indicate a possible solution. (2) It 
must be such that new data, instituted by observational operations 
directed by the provisional predicate (representing a possible so- 
lution), will unite with its subject-matter to form a coherent whole. 

6 The Newtonian theory of atoms represented a survival of the old conception 
of changeless substances. Within the context of the theory, however, they were 
transferred from the region of common sense objects to that of strictly scientific 
objects. 



US THE STRUCTURE OF INQUIRY 

The latter constitutes a substantial object in the logical sense of 
that term, or is on its way to becoming such an object. For it is 
union of connected distinctions so held together that it may be 
acted upon or with as a whole; and it is capable of incorporating 
into itself other predicated qualifications until it becomes, as 
such, a unity of inter-connected distinctions, or "properties." 

Take, for an example, such an elementary proposition as "this 
is sweet." This, as has been shown, marks a selective-restriction, 
made for a definite purpose, within an inclusive qualitative prob- 
lematic situation. The purpose is the final consequence of a 
resolved situation in attainment of which "this" has a special func- 
tion to perform. If the predicate "is sweet" is an anticipation of 
the resolved situation, it means "this" 'will sweeten something if 
that operation is performed which is required to generate definite 
perceptible consequence. Or, it may record the achieved result 
of the execution of the operation: "This has sweetened some- 
thing." When the operation is completed, this is definitely qualified 
as sweet. This fact is manifest not in a proposition (although a 
proposition may report it for purposes of record or communication 
of information) nor in symbols, but in a directly experienced 
existence. Henceforth, "this" is a sweet somewhat. The quality 
sweet does not stand alone but is definitely connected with other 
observed qualities. As thus characterized, it enters into further 
situations in which it incorporates into itself additional qualifica- 
tions. It is a sweet, white, granular, more or less gritty thing or 
substance, say, sugar. 

"Substance" represents therefore, a logical, not an ontological, 
determination. Sugar, for example, is a substance because through 
a number of partial judgments completed in operations which 
have existential consequences, a variety of qualifications so cohere 
as to form an object that may be used and enjoyed as a unified 
whole. Its substantial character is quite independent of its physi- 
cal duration, to say nothing of its immutability. The object, 
sugar, may disappear in solution. It is then further qualified; it is 
a soluble object. In a chemical interaction its constitution may 
be so changed that it is no longer sugar. Capacity for undergoing 
this change is henceforth an additional qualification or property 
of anything that is sugar. The condition — and the sole condition 



THE CONSTRUCTION OF JUDGMENT 129 

that has to be satisfied in order that there may be substantiality, 
is that certain qualifications hang together as dependable signs 
that certain consequences will follow when certain interactions 
take place. This is what is meant when it is said that substan- 
tiality is a logical, not a primary ontological determination. 

It is a form that accrues to original existence when the latter 
operates in a specified functional way as a consequence of opera- 
tions of inquiry. It is not postulated that certain qualities always 
cohere in existence. It is postulated that they cohere as depend- 
able evidential signs. The conjoined properties that mark off 
and identify a chair, a piece of granite, a meteor, are not sets of 
qualities given existentially as such and such. They are certain 
qualities which constitute in their ordered conjunction with one 
another valid signs of what will ensue when certain operations 
are performed. An object, in other words, is a set of qualities 
treated as potentialities for specified existential consequences. 
Powder is what will explode under certain conditions; water as 
a substantial object is that group of connected qualities which will 
quench thirst, and so on. The greater the number of interactions, 
of operations, and of consequences, the more complex is the con- 
stitution of a given substantial object. With the progress of 
technology, clay and iron have acquired new potentialities. A 
piece of iron is now a sign of many things of which it was not 
once a sign. When it was discovered that wood-pulp could be 
used for making paper if its material was subjected to operations in 
which it entered into new conditions of interaction, the signifi- 
cance of certain forms of lumber as objects changed. They did 
not become entirely new substantial objects because old poten- 
tialities for consequences remained. But neither was it the same 
old substance. The habit of supposing that it is the same all 
the time is the result of hypostatizing the logical character of 
being a sign or having significance into something inherent. Be- 
ing a substantial object defines a specific function. 

We speak regularly of chemical substances. A chemical sub- 
stance is represented not by enumeration of qualities as such, but 
by a formula which provides a synoptic indication of the various 
types of consequences which will result. The perceptible quali- 
ties of table sugar and sugar of lead are much the same. Even 



130 THE STRUCTURE OF INQUIRY ^ 

common sense learns to distinguish them as different "substances" 
in virtue of some of the different consequences which ensue from 
their operational use. In the scientific statement of their chemical 
substance, even common sensible qualities are ignored. Different 
formulae enable us to anticipate differences which are not sensibly- 
discernible at the time. To common sense, water is that which 
is potable, which will cleanse, upon which many things will float, 
etc. Chemically, it is H2O — a description in terms of a set of 
possible interactions and specified consequences. Some qualities 
are actually, sensibly, present. But as such they do not constitute 
an object. For common sense and for science alike, they consti- 
tute an object in virtue of the consequences of which the existent 
qualities, be they few or many, are signs, and of which they are 
the conditions provided operations institute certain interactions 
not then and there occurring. 

The contrast between the conception of substance that has 
been set forth here with the Aristotelian ontological conception 
is, of course, intimately connected with the great change which 
has taken place in science, i.e., its complete shift from immutable 
objects to correspondences of changes. Aristotle said, "It is absurd 
to make the fact that the things of this earth change and never 
remain the same the basis of our judgments about the truth. For 
in pursuing the truth one must start from things that are always 
in the same state and never change. Such are the heavenly bodies; 
for they do not appear to be now of one nature and now of an- 
other, but are always manifestly the same and do not change." 7 

Such immutable things alone were complete substances and fit 
to be subjects of "true" propositions. In present science, on the 
other hand, such transitory events as lightning and such variable 
things as the weather become subjects of scientific judgments when 
they are determined as constituents of a systematic set of changes 
which as changes are in functional correspondence. Such facts 
exemplify what is meant by the functional nature of substantial 
objects. In the light of dependable inferences that can be drawn, 
of the correlations of changes that are established, an event like a 
flash of lightning has logical solidity and endurance in spite of its 
existential transitivity. It is substantial. It is representable by a 

7 Aristotle, Metaphysics, 1063 % Ross' translation. 



THE CONSTRUCTION OF JUDGMENT 131 

substantive, which even when it is a verbal noun has constancy in 
discourse as a means of identification of the kind of which the 
singular is a specimen. 

IV. The Predicate of Judgment. The logical meaning of predi- 
cate has been anticipated in the discussion of the logical subject, 
because of the strict correlativity of respective existential and 
ideational contents. The meanings which are suggested as pos- 
sible solutions of a problem, which are then used to direct further 
operations of experimental observation, form the predicational 
content of judgments. The latter is related to the factual content, 
that is, the subject, as the possible to the actual. For example, 
in the illustration considered above, when "this 77 is estimated be- 
fore the act of tasting to be sweet, a certain consequence is an- 
ticipated to which is assigned a definite connection in the total 
situation. If, however, it is at once asserted "this is sweet," the 
assertion is logically premature and ungrounded. The anticipa- 
tion functions logically "to instigate and direct an operation of 
experimental observation. When the consequences of the latter 
combine with facts already ascertained so as to constitute a uni- 
fied total situation, inquiry comes to an end. But there is always 
danger that the congeniality or plausibility of the content of the 
predicate-meaning will lead directly to its acceptance. In that 
case, it is not operationally checked. It possesses logical status 
only as it is taken for what it is qua predicate — namely, a method 
of solution not itself a solution. There is also danger that pains 
will not be taken, even when an operation is performed, to scru- 
tinize its results in order to ascertain whether the existential con- 
ditions actually cohere in a unified way. These two failures are 
the common source of premature, hasty, and therefore ungrounded 
assertion. 

The essential error of the "rationalistic" tradition in logical 
theory consists in taking the consistency of the constituents of the 
conceptual contents (which form the predicate) as a final cri- 
terion of truth or assertibility. Subject-matter which, in its logical 
form, is a means for performing experimental activities to modify 
prior existences is mistaken to be final and complete in itself. 
Thereby an inherent ontological status is imputed to it. As has 
been pointed out, subject-matter endowed with "rational" form 



132 THE STRUCTURE OF INQUIRY 

was treated in classic logic as constituting a superior realm of 
"Reality," in comparison with which material capable of sensible 
observation was by Nature metaphysically inferior. The latter 
was "known" only in so far as it could be directly subsumed 
under the conceptual material. A more recent tendency is to 
regard the conceptual subject-matter as constituting a realm of 
abstract possibility also taken as complete in itself, not as indi- 
cating possibilities of operations to be performed. While the 
resulting metaphysical status assigned is very different from that 
of classic ontology, there is nevertheless the same hypostization 
of a logical function into a supra-empirical entity. Meantime, 
the practice of scientific inquiry has provided the foundations for 
a correct logical interpretation. 

The conceptual and "rational" contents are hypotheses. In 
their more comprehensive forms they are theories. As such they 
may be and usually are abstracted from application to this and 
that immediate existential situation. But on that very account, 
they are instruments of a wide, indefinite scope of operational 
application, actual application being made as special conditions 
present themselves. In reaction against the inherently "superior" 
position assigned to conceptual material, and because of its recog- 
nition of the necessity of observational experience to guarantee 
existential reference, "empiristic" logical tradition went to the 
other extreme. It denied the logical necessity of conceptual 
meanings and theories, reducing them to mere practical conven- 
iences. Traditional empiricism supposed it was following the 
pattern set by scientific inquiry. But in fact it was engaged in 
corrupting formulation of scientific inquiry by subjecting the 
latter to uncritically accepted conclusions of a subjectivistic 
psychological theory. 

V. The Copula. The logical import of copulation is involved 
in the prior account of subject and predicate. It is neither a 
separate and independent element nor yet does it affect the predi- 
cate alone, attaching the latter to an independently and externally 
given singular subject, whether the latter be taken to be an object, 
a quality, or a sense-datum. It does express the act of predica- 
tion. But it also expresses the act or operation of "subjection"; 
that is, of constituting the subject. It is a name for the complex 



THE CONSTRUCTION OF JUDGMENT 133 

of operations by means of which (a) certain existences are re- 
strictively-selected to delimit a problem and provide evidential 
testing material, and by which (b) certain conceptual meanings, 
ideas, hypotheses, are used as characterizing predicates. It is a 
name for the functional correspondence between subject and 
predicate in their relation to each other. The operations which 
it expresses distinguish and relate at the same time. 

The fact that judgment as such has a subject-predicate struc- 
ture, and that in this structure subject-and-predicate contents are 
at the same time distinguished and related, has been made a ground 
for holding that judgment has an inherently self-contradictory 
character. 8 This position is unanswerable unless it be recognized 
(1) that the copula stands for operations, and (2) that judgment 
is a process of temporal existential reconstitution. 

1. Inquiry demands, as we have seen, operations of both observa- 
tion and ideation. There would be no control of the process of 
inquiry if each of these operations were not expressly formed 
with reference to the other. It is easy to see what would 
happen if observation were directed to material which had no 
connection with entertained ideas and hypotheses, and if the latter 
went off on a track of their own, having no connection with the 
material obtained by observation. In the process of reasoning, 
especially in scientific inquiry, there is often a considerable period 
in which conceptual material is developed on its own account, 
leaving observed material temporarily in abeyance. But none- 
theless in controlled inquiry, the entire object of this seemingly 
independent development is to obtain that meaning or conceptual 
structure which is best adapted to instigate and direct just those 
operations of observation that will secure as their consequence 
just those existential facts that are needed to solve the problem 
in hand. 

2. Final judgment is attained through a series of partial judg- 
ments! — those to which the name estimates or appraisals has been 
given. Judgment is not something occurring all at once. Since 
it is a manifestation of inquiry, it cannot be instantaneous and 
yet be inquiry. Short of attainment of a finally resolved situa- 

8 For example, by F. H. Bradley in both his Logic and his Appearance and 
Reality. 



134 THE STRUCTURE OF INQUIRY 

tion (the result of final judgment and assertion) respective subject- 
and-predicate contents are provisionally instituted in distinction 
from and correlation with each other. Were subject-and-predi- 
cate contents final rather than provisional, distinction and relation 
would constitute a state of irreconcilable opposition. Since they 
are functional and operative, there is no more conflict than there is 
in the fact that in the course of every complex productive ac- 
tivity, industrial or social, divisions of labor are instituted which 
nevertheless are functionally connected with one another. For 
they are instituted as cooperating means of a common unified out- 
come. Were a complex undertaking in which extensive division 
of labor prevailed arrested short of its temporal issue, and were 
the various activities and their respective partial products taken 
at the moment of arrest to provide a final interpretation of what 
is going on, the conclusion might not be that there was inherent 
contradiction among them, but the idea that irrelevancy and dis- 
organization existed would be justified. The result of the discus- 
sion is, then, to show how indispensable it is to acknowledge that 
judgment, like inquiry, is temporal. It is temporal not in the 
external sense that the act of judging takes time, but in the 
sense that its subject-matter undergoes reconstitution in attaining 
the final state of determinate resolution and unification which is the 
objective that governs judgment. 

It is necessarily involved in what has been said that the linguistic 
form which expresses, or is the symbol of, judgment is a true 
verb; that is, one expressing action and change. 

When is appears in judgment it has temporal force, distinct from 
was or will be, and distinct from the "is" of a proposition where 
"is" designates a non-temporal or strictly logical relation between 
meanings. When it is stated that "the boy is running" the reference 
to change, time and place lies on the surface. When one says "this 
is red" the temporal reference is linguistically disguised. But the 
statement certainly does not mean that this is inherently red or is 
always red. Color quality changes to some extent with every 
change in light. It is red now, but only under a specifiable set of 
consequences, and a completely grounded judgment demands 
that the conditions be stated. "Is red" sets forth what in ordinary 
language is called an effect or a change brought about, or else a 



THE CONSTRUCTION OF JUDGMENT 135 

capacity to produce change, a power to redden other things. 9 

Etymologically, the word is derives from a root meaning to 
stand or to stay. To remain and endure is a mode of action. At 
least, it indicates a temporal equilibrium of interactions. Now 
a spatio-temporal change is existential. Consequently the copula 
in judgment, whether as a transitive or intransitive verb, or in the 
ambiguous form "is," has inherent existential reference. In such 
a proposition as "Justice is a virtue," is, on the other hand, stands 
for a relation between two abstractions or meanings, and accord- 
ingly is non-temporal. It is a mark of a logical relation such that 
in any proposition in which "justice" appears there is an im- 
plicatory relation to some proposition in which "virtue" appears. 10 
The situation to which the sentence refers determines unambigu- 
ously whether "is" has an active force, expressing a change going 
on actually or potentially, or whether it stands for a relation be- 
tween meanings or ideas. In a sentence having no contextual 
situation, its logical force is indeterminate. For any sentence iso- 
lated from place and function in inquiry is logically indeterminate. 
The copula in a judgment, in distinction from the term of 
formal relation, expresses, accordingly, the actual transformation of 
the subject-matter of an indeterminate situation into a determinate 
one. So far is the copula from being an isolable constituent that 
it might be regarded as what sets the subject-and-predicate con- 
tents at work executing their functions in relation to one another. 
In complex undertakings a plan for division of functions is usually 
laid out on paper. But this plan is not the actual division of labor. 
The latter consists in the actual distribution of the active factors 
of what is doing in their cooperation with one another. The dis- 
tribution, as well as the cooperation, is arranged with reference 
to an end or objective consequence. 

The plan may be set forth and explained in propositions; its 
propositional exposition may be a means of criticism and of re- 
arrangment of the plan of distribution. But the actual division 
can only be enacted. As just indicated, it may be stated in symbols, 
and symbolic representation of the division may be an indis- 

9 Cf . the previous analysis of "It is sweet." 

10 In other words, "the ambiguity of the copula," depends upon failure to 
determine whether in any given instance it has temporo-spatial reference or stands 
for a relation of meanings as such. 



136 THE STRUCTURE OF INQUIRY ^ 

pensable means of an actual enactment. But it no more is a func- 
tioning division of labor than a blueprint is a house in process of 
building or a map is a journey. Blueprints and maps are proposi- 
tions and they exemplify what it is to be propositional. Moreover, 
a map is no less a means of directing journeys because it is not 
constantly in use. Similarly, general propositions are no less a 
means of constructing judgments because they are not always op- 
erative in the existential work of reconstituting existential material 

Like a chart, indeed, like any physical tool or physiological 
organ, a proposition must be defined by its function. Further- 
more, there is the same sort of advantage in having conceptual 
frameworks manufactured and on hand in advance of actual oc- 
casions for their use, as there is in having tools ready instead of 
improvising them when need arises. Just as a complex under- 
taking in any field demands prepared materials as well as pre- 
pared instrumentalities, so propositions which describe conjunc- 
tions of existential materials — ultimately reducible to space-time 
connections — are required in effective inquiry. At the outset 
substantial object-events serve this purpose as more or less sec- 
ondary by-products or deposits from prior inquiries. But finally 
they are deliberately constituted by critical inquiry intended to 
produce objects that will operate as effective and economical 
means when they are needed — a differentia of common sense and 
scientific objects. Propositions about subject-contents, about 
spatial-temporal conjunctions of properties of existence, thus un- 
dergo independent development just as do propositions about 
meanings and their relations. The former will be called material 
means and the latter procedural means, it being remembered that 
both are operational since they are means of determining the final 
situation and judgment. 

Despite the decay and abandonment of the cosmological foun- 
dation of the Aristotelian theory of the structure and the constitu- 
ents of judgment, conceptions which were essential to it still play 
an important part in many logical texts under the name of the 
theory of predicables. That which can be predicated was classified 
in respect to its logical force or form under the following heads: 
essence, property, genus, differentia and accident. They ex- 
pressed the ways in which predication can take place because of 



THE CONSTRUCTION OF JUDGMENT 111 

the different kinds of connection that were supposed to exist among 
things. 

A substantial species is what it is in virtue of its eternal and 
fixed essence. To predicate an essence of a substance is accord- 
ingly to define it, definition being, as previously noted, neither 
verbal nor an aid in inquiry, but an apprehension ("re-marking" 
in a literal sense) of that which makes the substance to be what 
it is. A definition is stated and communicated by means of the 
predicables, genus and differentia, these being logical, not onto- 
logical like species and essence. A genus differed from a species; 
it was not, as in modern theory, simply a kind that is more compre- 
hensive than the kinds called species. It has no existence while 
a species must be. It cannot, therefore, be the subject of any 
final judgment. 11 

Plane figure is generic as compared with triangle, and triangle 
is generic with respect to isosceles, scalence and right-angle tri- 
angles. But even the latter were only qualifications of species 
existing in nature. In setting forth a definition, in leading another 
to learn to grasp a defining essence or in enabling one's self to 
regrasp it, we start with the proximate genus and then give the 
differentia which distinguish a species within that genus from 
every other species falling within it. Thus the differentia of the 
genus plane figure in the case of a triangular figure is having three 
sides. A genus is the logical "matter" of definition, related to it 
as potentiality is to actuality in ontological material. 

A property is no part of an essence but flows necessarily from 
it. It may, therefore, be predicated universally and necessarily 
of a subject just as the defining essence may be. It is not part 
of the essence of man to be a grammarian. But it flows neces- 
sarily from the essence of man as rational. Theorems that flow 
from the definitions and axioms of the Euclidean geometry have 
a similar logical status. But some things can only be predicated 
accidentally — that is, when they are neither part of an essence 
nor flow from it, nor are of the nature of genus and differentia. 
All changing things which cannot be enclosed within fixed limits 

11 Upon its logical side, the Aristotelian polemic against Platonic Ideas and 
Numbers (geometrical figures) was based upon the fact that the latter are genera, 
not species, and hence cannot exist by themselves, but only in thought. 



138 THE STRUCTURE OF INQUIRY 

are of this character. They bear a purely contingent relation to 
that of which they are predicated. It may be affirmed that "most 
blue-eyed persons are blonde"; "days in summer are warm as a 
rule or upon the whole"; etc. But there is no necessary connec- 
tion between subject and predicate. They just happen, as it were, 
to be that way — not in the sense that there is no cause for their 
happening that way rather than in some other way, but in that 
the cause is itself another change, which also has a contingent 
relation to what is permanent, universal and necessary. There is 
no reason why accidents occur as they do in the sense of reason 
proper to the Aristotelian scheme. 

This theory of the forms of predication was acute and com- 
prehensive under the scientific conditions in which it was for- 
mulated. In the light of the theory and practice of modern 
scientific inquiry it has no validity. I shall take one instance as 
exemplary. Seeming exceptions to law or general principle ("ac 
cidents" in the old sense) are now the nutriment upon which 
scientific inquiry feeds. They have a ground or "reason" in the 
correlated conditions of their occurrence. General propositions 
are not only possible about these correlations but every existential 
general proposition or law is about them. In any other sense of 
the word, that which is "accidental" is that which is irrelevant in 
any given situation, and which, therefore, is to be ruled out be- 
cause of absence of evidential function in the given problem. If 
not ruled out it is likely to carry inquiry into a wrong track. In 
short, there are no prior fixed and ready-made determination of 
what may be predicated and of ways of predication. Every 
predicate is ideational or conceptual. It must be so constituted as 
to direct operations whose consequences throw light upon the 
problem dealt with and provide additional evidence for its solu- 
tion. Apart from the limits set by the problem in hand, there are 
no rules whatever for determining what may or should be predi- 
cated. As far as present logical texts still continue to take about 
essences, properties and accidents as something inherently different 
from one another, they are repeating distinctions that once had an 
ontological meaning and that no longer have it. Anything is "es- 
sential" which is indispensable in a given inquiry and anything is 
"accidental" which is superfluous. 



CHAPTER VIII 

IMMEDIATE KNOWLEDGE: 

UNDERSTANDING AND INFERENCE 



^he considerations adduced in discussion of the pattern of 
inquiry and of the structure of judgment, entail the con- 
, elusion that all knowledge as grounded assertion involves 
mediation. Mediation, in this context, means that an inferential 
function is involved in all warranted assertion. The position here 
defended runs counter to the belief that there is such a thing as im- 
mediate knowledge, and that such knowledge is an indispensable 
precondition of all mediated knowledge. Because of the wide cur- 
rency of this latter doctrine and the intrinsic importance of the 
logical issue involved, this chapter will be devoted to the discussion 
of the theme of immediate knowledge. 

Logical schools as opposed to each other as are the rationalistic 
and the empiristic agree in accepting the doctrine of immediate 
knowledge. On this point they differ only with respect to the 
objects and organs of such knowledge. Rationalist schools hold 
that ultimate principles of a universal character are the objects of 
immediate knowledge and that reason is the organ of their ap- 
prehension. Empiristic schools believe that sense-perception is 
the organ of knowledge and that the things immediately known 
are sensory qualities or, as they are now more usually called, 
sense-data. Some logical theories maintain that both kinds of 
immediate knowledge exist and that mediation and inferential 
knowledge result from the union of the two; a union in which 
a priori first truths and empirical material are brought into con- 
nection with each other. 

The doctrine of immediate knowledge would not be so widely 
held unless there were prima facie grounds of great plausibility to 

139 



140 THE STRUCTURE OF INQUIRY 

suggest it and apparent evidence that can be marshalled in its 
support. I shall introduce critical discussion of the doctrine by 
stating how these grounds are to be interpreted from the stand- 
point of the position already taken in this book. 

1. There is continuity in inquiry. The conclusions reached in 
one inquiry become means, material and procedural, of carrying 
on further inquiries. In the latter, the results of earlier inquiries 
are taken and used without being resubjected to examination. In 
uncritical reflection the net outcome is often an accumulation of 
error. But there are conceptual objects, and objects of perceptual 
experience, which have been so instituted and confirmed in the 
course of different inquiries, that it would be a waste of time and 
energy in further inquiries to make them objects of investigation 
before proceeding to take and use them. This immediate use of 
objects known in consequence of previous mediation is readily 
confused with immediate knowledge. 

2. It was noted in the previous chapter that final judgment is 
constructed by a series of intermediate partial judgments, to which 
the name estimates or appraisals was given. The content of these 
intermediate judgments, which cover both matters of fact and 
conceptual structures, is carried in propositions. In any inquiry 
of extensive scope (because of the nature of the problem with 
which it is concerned) these propositions gain relative inde- 
pendence. While they are ultimately means for determining final 
judgment, for the time being they are absorbing ends; just as, we 
have seen, in physical production and construction, tools are 
apparently independent objects complete and self-sufficient in 
themselves. Their function and the potential consequence of the 
exercise of their function become completely integrated into their 
immediate structure. As soon as it is forgotten that they are 
means and that their value is determined by their efficacy as oper- 
ative means, they appear to be objects of immediate knowledge 
instead of being means of attaining knowledge. 

When, however, their functional character is recognized, the 
mistake which is committed in these interpretations is evident: 

1. While the direct use of objects, factual and conceptual, 
which have been determined in the course of resolving prior 
problematic situations is of indispensable practical value in the 



IMMEDIATE KNOWLEDGE 141 

conduct of further inquiries, such objects are not exempt in new 
inquiries from need for reexamination and reconstitution. The 
fact that they have fulfilled the demands imposed upon them in 
previous inquiries is not a logical proof that, in the form in which 
they have emerged, they are organs and instrumentalities which 
will satisfy the demands of a new problematic situation. On the 
contrary, one of the commonest sources of error is the premature 
assumption that a new situation so closely resembles former ones 
that conclusions reached in these earlier cases can be directly 
carried over. Even the history of scientific inquiry shows how 
often this error has been made and for what long periods it has 
gone undetected. One indispensable condition of controlled in- 
quiry is readiness and alertness to submit the conclusions of even 
the best grounded conclusions to re-inquiry with reference to their 
applicability in new problems. There is a presumption in their 
favor but the presumption is no guarantee. 

2. A similar order of considerations applies to propositional 
contents which are taken and used. They may have proved 
completely valid in dealing with some problems and yet not be 
the fit means for dealing with problems which prima facie present 
the same features. One may point to the revisions of the proposi- 
tions of classic mechanics that were required when applied to ex- 
tremely minute bodies of high velocities. For centuries, the axioms 
and definitions of Euclidean geometry were regarded as absolute 
first principles which could be accepted without question. Preoc- 
cupation with a new order of problems disclosed that they were 
both overlapping and deficient as logical grounds for a generalized 
geometry. The result has made it clear that instead of being 
"self-evident" truths immediately known, they are postulates 
adopted because of what follows from them. In fact, the belief 
that they are true by their intrinsic nature retarded the progress 
of mathematics because it prevented freedom of postulation. With 
this change in the conception of the character of mathematical 
axioms, one of the chief bulwarks of immediate knowledge of uni- 
versal principles crumbled. 

The denial of the existence of immediate knowledge does not 
then deny the existence of certain facts alleged to support the 
doctrine. It is the logical interpretation of these facts which is 



142 THE STRUCTURE OF INQUIRY 

in question. Denial of the particular interpretation now under 
critical discussion was positively foreshadowed in the considera- 
tions which established the provisional and operational standing 
of the factual and conceptual contents of judgment. It is no- 
torious that a hypothesis does not have to be true in order to be 
highly serviceable in the conduct of inquiry. Examination of 
the historical progress of any science will show that the same thing 
holds good of "facts": of what has been taken in the past as evi- 
dential. They were serviceable, not because they were true or 
false, but because, when they were taken to be provisional work- 
ing means of advancing investigation, they led to discovery of other 
facts which proved more relevant and more weighty. Just as it 
would be hard to find an instance of a scientific hypothesis that 
turned out to be valid in precisely the same form in which it was 
first put forward, so it would be hard in any important scientific 
undertaking to find an initial proposition about the state of facts 
that has remained unchanged throughout the course of inquiry 
in respect to its content and its significance. Nevertheless, propo- 
sitions about hypotheses and about conjunctions of existences have 
served an indispensable purpose because of their operational char- 
acter as means. The history of science also shows that when 
hypotheses have been taken to be finally true and hence un- 
questionable, they have obstructed inquiry and kept science com- 
mitted to doctrines that later turned out to be invalid. 

These considerations dispose of a dialectical argument which 
has been used ever since the time of Aristotle, and is still current 
today. It is argued that inference must rest upon something 
known from which it starts, so that unless there are true premises 
which serve as such a basis it is impossible, no matter how adequate 
inference and discursive reasoning may be, to arrive at true con- 
clusions. Hence the only way of avoiding a regressus ad Infinitum 
is said to be the existence of truths immediately known. Even if 
the argument were dialectically unanswerable, it would still be con- 
fronted by the stubborn facts which show that correct conclusions 
have been progressively reached from incorrect "premises." But 
the dialectical reply is simple. It suffices to have hypothetical 
(conditional) material such that it directs inquiry into channels 
in which new material, factual and conceptual, is disclosed, ma- 



IMMEDIATE KNOWLEDGE 143 

terial which is more relevant, more weighted and confirmed, more 
fruitful, than were the initial facts and conceptions which served 
as the point of departure. This statement is but a restatement of 
the functionally operative status of the contents of judgment up 
to enactment of final judgment. 

A certain ambiguity in words has played a very considerable 
role in fostering the doctrine of immediate knowledge. Knowl- 
edge in its strictest and most honorific sense is identical with war- 
ranted assertion. But "knowledge" also means understanding, and 
an object, or an act (and its object) that may be — and has been 
— called apprehension. I can understand what the word and the 
idea of centaur, sea-serpent, transmutation of chemical elements, 
mean, without thereby knowing them in the sense of having 
grounds for asserting their existence. No intelligent search for a 
new invention, no controlled inquiry to discover whether a certain 
conception of, say, the nature of atoms is or is not borne out by 
the hcts, can be conducted without a direct grasp or understand- 
ing of the meaning-content of some idea. As the very descrip- 
tion of this kind of "knowledge" shows, it is not knowledge in the 
sense of justified assertion that a state of existence is thus-and-so. 
It is easy, however, as the history of philosophy illustrates, to 
carry over the first meaning into the second. Since the first is 
direct or immediate when it occurs, it is assumed that the second 
also has the same properties. Just as, after considerable experience, 
we understand meanings directly, as when we hear conversation 
on a familiar subject or read a book, so because of experience we 
come to recognize objects on sight. I see or note directly that 
this is a typewriter, that is a book, the other thing is a radiator, 
etc. This kind of direct "knowledge" I shall call apprehension; 
It is seizing or grasping, intellectually, without questioning. But 
it is a product, mediated through certain organic mechanisms of 
retention and habit, and it presupposes prior experiences and me- 
diated conclusions drawn from them. 

But the important point for the purpose of the present topic is 
that either an immediate overt response occurs, like using the 
typewriter or picking up the book (in which cases the situation 
is not a cognitional one), or that the object directly noted is part 
of an act of inquiry directed toward knowledge as warranted 



144 THE STRUCTURE OF INQUIRY 

assertion. In the latter case, the fact of immediate apprehension 
is no logical guarantee that the object or event directly appre- 
hended is that part of the "facts of the case" it is prima facie 
taken to be. There is no warrant for assuming that it is evidential 
with respect to the final assertion to be reached. It may be ir- 
relevant in whole or part, or it may be trivial in its significance for 
the problem in hand. Its very familiarity may be obstructive, 
tending to fix indications that are suggested in old grooves when 
the need is to search for data which will start suggestions in an 
unaccustomed direction. In other words, immediate apprehension 
of an object or event is no more identical with knowledge in the 
logical sense required than is immediate understanding or co7n~ 
prehension of a meaning. From these general considerations, I 
turn to an examination of certain theories of immediate knowledge 
which have exercised historical influence. 

I. The Empiristic Theory of Mill. Mill denies that there are 
general self-evident truths, or general a priori truths. Since he 
does not deny the existence of general truths, he is committed to a 
statement of a theory concerning their grounds or "proof." 
His position on this point is unambiguous. They not only arise, 
genetically, in the course of sense perception, but they are proved, 
if proved at all, by means of such particulars. These particulars, 
in so far as they are ultimate, are then immediately known. For 
them to exist in sense-perception is identical with their being 
known. When this statement does not itself appear to be self- 
evidently true, it is said to be such because we are dealing with com- 
plexes of particulars, not with ultimate simple particulars. The 
latter Mill calls indifferently sensations or feelings, or even states 
of consciousness which are known when and because they exist. 
"Truths," he says, "are known in two ways: some are known 
directly, and of themselves; some through the medium of other 
truths. . . . The truths known by intuition are the original 
premises from which all others are inferred. . . . The province 
of logic must be restricted to that portion of our knowledge 
which consists of inferences from truths previously known. . . / 
Examples of truths known to us by immediate consciousness are 
our bodily sensations and mental feelings. I know directly and of 

1 John Stuart Mill, Logic, Introduction, Sec. 4. 



IMMEDIATE KNOWLEDGE 145 

my own knowledge, that I was vexed yesterday, or that I am 
hungry today." 2 

The question of whether states of consciousness exist which 
necessarily "know" themselves in virtue of being states of con- 
sciousness, Mill calls "metaphysical." In reality, the belief in then- 
existence was part of a provincial psychological tradition; it no 
longer generally obtains. His position in respect to "immediate" 
knowledge of particulars can be discussed, however, without 
reference to any special assumption concerning the constitution 
of the particulars. Leaving out all reference to sensations and 
states of consciousness, it should be obvious that his examples fall 
far short of exemplifying what he alleges they illustrate. 

Take the phrase "I was vexed yesterday." The meaning of "I" 
is so far from being immediately given that it has long been the 
theme of controversial discussion; an immediate knowledge of 
"yesterday" is certainly an extraordinary occurrence; differentia- 
tion of "vexation" from other emotional states is a rather slow 
acquisition in human development. The case is no different in 
principle from "I am hungry today." It is possible to feel hungry 
when one is not hungry; the "feeling" can be produced artificially 
without the organism being in a state of need for food. The 
discrimination between the two states may be a difficult problem. 
If "today" means anything more than the present moment, it 
involves a fairly elaborate intellectual construction, and any 
number of passages could be quoted from Mill himself to the 
effect that a given immediate state can be characterized as hunger 
only by going beyond that state and assimilating it inferentially to 
other states. That common sense directly grasps certain occur- 
rences as having the significance of vexation, hunger, yesterday, 
today, is undeniable. But the "self -evidence" bred by familiarity, 
while a fact of practical importance, is very different from cogni- 
tive self -evidence, and often leads common sense astray even in 
practical matters. We are forced to the conclusion, which a more 
detailed analysis would bear out, that Mill's whole doctrine of 
immediate-knowledge is itself an inference from a psychological 
theory which is itself inferential. In its strictly logical bearing it 
rests upon the uncritical acceptance of the old notion that no 
2 John Stuart Mill, Logic, loc. ck. 



H6 THE STRUCTURE OF INQUIRY __^ 

proposition can be "proved" unless it follows from "truths" al- 
ready known. 

II. The Lockeian Version. Locke's account of immediate 
knowledge is important not only because of its historic influence, 
in that his original objective view of sensations and ideas was the 
source of their later transformation into states of consciousness, but 
because of his clear grasp of the epistemic issue involved — an 
issue that was obscured and dodged in later developments. He 
holds, on the one hand, that all knowledge of material existence 
depends upon sensation, and he points out, on the other hand, 
that sensations (which he takes to be bodily states) come between 
us and knowledge of objects in nature in such a way as to render 
impossible scientific knowledge of the former. In the first place, 
most sensory qualities do not belong to natural objects, which 
possess only the primary qualities of figure, size, solidity and 
motion; in the second place, even the latter as experienced qualities 
do not enable us to get knowledge of the "real constitution" of 
objects. 

"If," says Locke, "we could discover the figure, size, texture 
and motion of the minute constituent parts of any two bodies we 
should know without trial [experience] several of their operations 
upon one another as now we do know the properties of a square 
or triangle." But "if" here represents a condition contrary to fact. 
For we are destitute of senses acute enough to discover the minute 
particles of bodies and to give us ideas of their mechanical con- 
stitution. Nor is this the whole story. Even if we had senses 
acute enough to meet this condition (and it might now be argued 
that recent physics with the aid of artificial devices has supplied 
the lack), the dependence of knowledge of the real constitution of 
objects upon sense would still stand immovably in the way. 
"Knowledge about natural objects extends as far as the present 
testimony of the senses employed about particular objects that do 
then affect them and no further. Hence, we shall never be able 
to discover general, instructive, unquestionable truths about natural 
objects." 3 The italicized words, present and then indicate the 
impassable barrier existing between sense, which is particular and 

3 John Locke, Essay on the Human Understanding, Book IV, Ch. 3 on the 
Extent of Knowledge. 



IMMEDIATE KNOWLEDGE 147 

transient, and objects which are permanent and have identical 
ultimate "constitutions" or structures. 

This thoroughgoing negative conclusion of Locke, which neces- 
sarily follows from regarding sense-data as themselves objects of 
knowledge, might have acted as a warning to later theorists against 
assigning inherent cognitive import to sense-data; as a warning to 
examine any premise that leads to the conclusion that knowledge 
of physical objects is impossible. If sense-data, or any other data, 
are final and independent (isolated) objects of knowledge, then 
no predicates having objective existential reference can be war- 
rantably attached to them. 

At times, when Locke rebels at his own conclusion, and is 
desirous of justifying the ways of God and Nature to man, he lays 
down a principle which, if he had followed it out consistently, 
might have set subsequent theory upon a different track. Upon oc- 
casion he says that qualities are marks of differences in things 
"whereby we are able to discern one thing from another, and so 
choose them for our necessities and apply them to our uses" — as, 
say, the quality of white, which enables us to tell milk from water. 4 

Had this mode of interpretation of sensory qualities been made 
fundamental, it would have appeared that they are not objects 
of cognition in themselves but that they acquire cognitive func- 
tion when they are employed in specific situations as signs of some- 
thing beyond themselves. Qualities are the sole means we have 
for discriminating objects and events. Their use in this capacity 
is constant. For practical purposes no harm results in identifying 
the function with the quality as an existence, just as no harm re- 
sults from identifying an object as a spade because the operative 
use and the consequences of the use of the object are integrated 
with its existence. But failure for the purposes of theory to dis- 
tinguish existence and function has been the source of continued 
doctrinal confusion. 

III. Atomic Realism. Mill's interpretation suffered as we saw 
from two serious blemishes. It regarded qualities as states of 
consciousness and it treated such complex objects as today, yester- 
day and vexation as simple primitive data. Recent theory has 
avoided both of these errors. Qualities are given objective status 

4 Ibid., Book IV, Ch. 4, on the Reality of Knowledge. 



148 THE STRUCTURE OF INQUIRY 

as sense-data, and the supposedly immediately given existential 
contents of propositions are treated as complexes to be reduced to 
data that are irreducibly simple. Apprehension of immediate 
simple qualities constitutes propositions which are "atomic," while 
propositions containing an inferential coefficient are "molecular." 
Such propositions as "This is red, hard, sweet," etc., are atomic. 
According to the theory, this in such propositions is devoid 
of any descriptive qualification. For were this anything more 
than a bare demonstrative, it would be complex and hence, on 
the theory, not immediately given. In "This ribbon is red," what 
is designated by ribbon is not given in the sense in which "this" 
and "red" are given. Some writers also include in the domain of 
atomic propositions, such propositions as "This is before that" as 
a simple and ultimate immediately given relation. 

The notion that there is such a thing as a merely demonstrative 
"this" lacking all descriptive content has already been criticized. 
According to the atomic logical theory, each this, as a subject of a 
proposition, must be exactly identical logically (though not in 
quality) with every other. Each is determined by the mere act of 
pointing at and each such act contains, by statement, nothing that 
marks it off from any other demonstrative act. It follows that 
there is no ground or reason for predicating one quality of it 
rather than any other. The case is not bettered if it is said that 
"this red" is what is irreducibly given. For even here we have no 
proposition, only a bare "subject" which is the subject of no 
predicate. As in the first case, there is no ground whatever for 
any determinate predication. 

It would not be denied, I suppose, that in fact it requires a 
series of experimental operations, involving definite techniques, 
to warrant the assertion that a given present quality is red. A 
scientific determination differs from a loose common sense asser- 
tion of the existence of a specific quality just in the fact that such 
techniques are employed. A strictly grounded scientific de- 
termination of red would, for example, involve the techniques by 
means of which the presence of a definite number of vibrations 
per unit of time was ascertained. In other words, it is not held, I 
take it, that the atomic quality is primitive in a psychological sense. 
It is logically primitive in that any existential proposition finally 



IMMEDIATE KNOWLEDGE 149 

rests upon determination of some simple quality. Now, while in 
most cases inquiry does not actually go as far as this, it is admitted 
that in theory experimental observation must proceed to determine 
an irreducible quality in order that an existential proposition be 
fully warranted. But the more clearly this fact is recognized the 
more clearly does it stand out that such a determination is not 
complete and final in itself but is a means to the resolution of some 
problem. It is a factor in the institution of what may warrantably 
be taken and used as evidence. For example, consider the case in 
which the utmost pains are taken in a case of spectrum analysis to 
reach a grounded proposition that such-and-such a color quality is 
present. 

The fallacy in the theory of logically original complete and self- 
sufficient atomic propositions is thus an instance of the same fallacy 
that has been repeatedly noted: The conversion of a function in 
inquiry into an independent structure. It is an admitted fact that 
ideally, or in theory, propositions about irreducible qualities are 
necessary in order adequately to ground judgment having existen- 
tial reference. What is denied is that such propositions have com- 
plete and self-sufficient logical character in isolation. For they are 
determinations of evidential material in order to locate the problem 
in hand and secure evidence to test a solution. The doctrine 
under criticism rules out the context in which such propositions 
occur and the logical end for which and logical ground upon 
which they are instituted. This may be verified by any one who 
calls to mind a case in which, either in common sense or science, 
such propositions are present and have weight. As to their 
ground, I call attention again to the fact that there is no this which 
is merely and exclusively red or any other single quality and that, 
therefore, there must be some ground for selection of one quality 
as predicate rather than another. 

Although further discussion of the logical principles involved 
will require some retraversing of matters already gone over, the 
basic importance of the issue justifies repetition, especially as the 
territory will be surveyed from a somewhat different point of 
view. It has been usual for some time in philosophy (1) to view 
the common sense world in its distinction from the domain of 
scientific objects as strictly perceptual in character; (2) to regard 



150 THE STRUCTURE OF INQUIRY 

perception as a mode of cognition; and (3) what is perceived 
whether object or quality, to be therefore cognitive in status and 
force. None of these assumptions is warranted, (a) The common- 
sense world includes, to be sure, perceived objects, but these are 
understood only in the context of an environment. An environ- 
ment is constituted by the interactions between things and a living 
creature. It is primarily the scene of actions performed and of 
consequences undergone in processes of interaction; only secondar- 
ily do parts and aspects of it become objects of knowledge. Its 
constituents are first of all objects of use and enjoyment-suffering, 
not of knowledge, (b) In relation to perception, an environment 
forms an extensive temporal-spatial field. Only occasionally are 
reflexes directed in the life behavior of an organism toward isolated 
excitations. The maintenance of life is a continuous affair. It 
involves organs and habits acquired in the past. Actions performed 
have to be adapted to future conditions or death will speedily 
ensue. The material towards which behavior is directly impelled 
is but the focal aspect of an environing field. The kind of be- 
havior which occurs must, in order to be adaptive and responsive, 
vary with the kind of field of which the immediate object is focal. 
It follows, then, that when objects or qualities are cognitively 
apprehended, they are viewed in reference to the exigencies of the 
perceived field in which they occur. They then become objects 
of observation, observation being defined precisely as the 
restrictive-selective determination of a particular object or quality 
within a total environing field. Usually the total environing 
field is "understood," or taken for granted, because it is there as 
the standing condition of any differential activity to be performed. 
The psychological theory of perception has been framed in terms 
of what happens in these specific differential acts of observation- 
perception of an object or a quality, an orange, a patch of yellow. 
For the purpose of a report of just what occurs in an observation 
and for the psychological problem involved, it is not necessary to 
criticise this procedure. But when the results are carried over into 
logical theory and taken to provide the basis for a theory of data 
in their logical status and bearing, complete distortion results. 
For isolated objects or qualities are then taken in their isolation to 
be the givens or data. 



IMMEDIATE KNOWLEDGE 151 

For logical purposes, it makes no difference whether the data, 
when reduced to their simplest contents, are taken to be Lockeian 
simple ideas, sensations, Humeian impressions, the sense-data of 
contemporary theory, or "essences." For the same isolation, self- 
sufficiency, and completeness is ascribed to them in each case. 
What has actually occurred, then, in the formation of the con- 
temporary theory of atomic propositions is that the conclusions of 
psychological theory, reached in dealing with a special psycho- 
logical situation, have been bodily transferred into logic and made 
the basis of the entire doctrine of atomic propositions having 
existential reference. This uncritical adoption of psychological 
conclusions as the foundation of an important branch of the logical 
theory of propositions has occurred in spite of the fact that the 
logicians who proceed in this way are particularly urgent about 
the necessity of freeing logic completely from psychological 
matters. 5 

I turn now to certain popular and empirical considerations 
which are taken to substantiate the notion of immediate knowl- 
edge. 1. The distinction between acquaintance-knowledge and 
knowledge-about and the validity of the distinction is generally 
acknowledged. I am acquainted with my neighbor; I know some- 
thing about Julius Caesar. Acquaintance-knowledge has a direct- 
ness and intimacy lacking in knowledge-about. The latter can 
only be expressed in propositions that certain things are so-and-so. 
The former is expressed in actual commerce with the individual; 
it is marked by affection and dislikes. It takes effect in expecta- 
tions as to the conduct of the person or object with which one is 
acquainted so that appropriate ways of overt conduct are ready in 
advance in the person having the acquaintance. I am acquainted, 
say, with the French language when I am prepared to speak and 
read it; I may know about its grammar and something of its 
vocabulary and yet have no ability to speak. The distinction be- 
tween the two modes of knowledge was embodied in linguistic 
expressions long before theoretical attention was called to it: 
Cognoscere and scire; connaitre and savoir; konnen and <wi$sen; 

5 A by-product of this dependence upon a special psychological analysis is that 
the doctrine of atomic propositions as ultimate existential propositions makes 
necessary the assumption of a priori universal propositions, for the atomic proposi- 
tions, by description, are incapable of grounding inference and reasoning. 



152 THE STRUCTURE OF INQUIRY 

in earlier English idiom, to ken (with its association of can, ability 
to act) and to wit. 

The existence and the importance of the difference is acknowl- 
edged. But it is far from supporting the logical theory of im- 
mediate knowledge. The immediacy involved is that of intimate 
connection with emotion and ability to act. In the first place, 
acquaintance-knowledge is not primitive, but acquired, and in so 
far depends upon prior experiences into which mediation has 
entered. In the second place (and of more importance for the 
present point), acquaintance-knowledge is frequently not knowl- 
edge in the sense of being warrantably assertible. It enables us 
to form practical expectations which are perhaps often fulfilled. 
But the familiarity that attends acquaintanceship often blinds us 
to things of primary importance in reaching conclusions. Ac- 
quaintance with certain habits of speech is no guarantee against 
blunders and solecisms; it may be their source. From a logical 
point of view acquaintance-knowledge is subject to critical in- 
quiry and revision. As a rule, it invites it. 

2. The existence of recognitions, which are practically in- 
stantaneous, is another empirical ground for the theory under 
examination. The same considerations apply here as in the case 
of acquaintance-knowledge. In fact, recognition may be re- 
garded as a special limiting instance of the latter. We recognize 
persons with whom we have only slight acquaintance; we may 
recognize words in a foreign language without being so acquainted 
with the language that we can speak or read it. Recognition of an 
object is also (a) a product of experiences which have involved 
doubt and search, and (b) while of immense practical importance, 
is not exempt from the necessity of inquiries to determine the 
correctness of a given recognition and its pertinency to the 
problem in hand. Recognition is not re-cognition in the sense of a 
re-knowing. It is rather an acknowledgement of a certain object 
or event as having a specified place in a situation. 

The doctrine that "simple apprehension" is complete in itself is 
often accompanied by a certain fallacy. It is supposed that because 
the act of apprehension is simple and single, therefore, the object 
apprehended must also be. But complex scenes are also appre- 
hended simply — as when one returns to the scene of his childhood. 



IMMEDIATE KNOWLEDGE 153 

Moreover, relatively simple objects are important not in virtue of 
their inherently simple structure but because of some crucially 
evidential role their simplicity permits them to play — as for ex- 
ample, in the relation of finger-prints to personal identifications. 
Similarly, we recognize a familiar person by his voice alone with- 
out having to observe him in his physical entirety. It saves time 
and energy to be able to make the relatively simple a means of 
identification. 

Such facts suggest the peculiar function of simples or elements 
in inquiry. The more complex the structure of an object, the 
greater the number of possible inferences that can be drawn 
from its presence; its different constituents point in different 
directions. The less complex a given object or event the more 
restricted it is in its constitution and hence the more definite is its 
indicative signifying capacity. There is abundant evidence in the 
history of science to show that reduction of objects to elements is 
one of the most effective means of both safeguarding and extend- 
ing inferential inquiry. There is no evidence that such simple 
elements exist by themselves in nature. It is foolish to object to 
analysis and its outcome in institution of elements. But the very 
foolishness of this objection goes to show that the concept of 
"simple" and "element" is functional and that giving simples and 
elements independent existential standing, whether in physics, 
psychology, anatomy or politics, is but one more case of hypostiza- 
tion of an instrument. 

IV. Understanding and Comprehension. So far the detailed 
discussion has been occupied with existential subject-matters, for 
grasp of which the word apprehension is generically employed. 
It is advisable to say something about direct grasp of meanings 
and conceptual structures for whose designation the words under- 
standing or comprehension is used. We take, see, and "twig," 
the force of an argument; we have insight into general principles. 
The seeing and insight are often direct and practically instantane- 
ous. A meaning, previously obscure, may come to us "in a flash." 
The same type of considerations adduced with respect to direct 
apprehension of objects and qualities applies in the case of the 
present topic, and discussion may be abbreviated. Attention has 
already been called to the fact that one meaning of to know is to 



154 THE STRUCTURE OF INQUIRY 

understand, and that this meaning is not to be confused with 
warranted affirmation of validity. A person must understand the 
meaning of authorship in order to consider intelligently the ap- 
plication of that term to a given person, say, of the Waverley 
Novels. The understanding is a necessary condition of any 
particular ascription having validity. But evidently it is not a 
sufficient condition. 

The series of propositions which constitute a chain of ordered 
discourse should be such that the meanings of their constituent 
terms are as unambiguous and determinate as possible. But ful- 
filment of this condition does not guarantee the validity of their 
application in a given problem. Hence understandings like appre- 
hension, is never final. No proposition about a relation of mean- 
ings, however determinate and adequate the proposition is, can 
stand alone logically. Nor is its incapacity to stand alone re- 
moved by union with other propositions of the same sort; although 
the union may result in getting meanings into such a shape that 
they are fitted for application. 

The two doctrines, that there is an immediate knowledge of 
existential objects or of qualities as sense-data, and that there is an 
immediate knowledge of rational principles — necessarily go to- 
gether. Atomistic empiricism and rational a priorism are cor- 
relative doctrines. Kant's categories of the a priori understanding 
are the logical counterpart of the doctrine of independent sense- 
material which he took over from Hume, just as T. H. Green's 
"necessary relations of thought" are required to balance the view 
of sensations he took over from the psychology of the school of 
the Mills. When the existential material of experience is reduced 
to immediately given atomic cases of "this," connection between 
the atoms (such as is involved in every molecular proposition), 
is impossible unless non-empirical or a priori propositions are recog- 
nized. Postulation of self-evident existential "facts" requires 
postulation of self-evident rational "truths." 

A strictly logical formulation of this state of affairs is given by 
Bertrand Russell. After stating that "in every proposition and in 
every inference there is, besides the particular subject-matters 
concerned, a certain -forvi, a way in which the constituents of the 
proposition are put together," he gives the following example of 



IMMEDIATE KNOWLEDGE 155 

what is meant by form: "If anything has a certain property, and 
whatever has this property has a certain other property, then the 
thing in question has the other property." He then goes on to 
draw the theoretical conclusion considered in the next paragraph. 6 

The proposition cited as an example of form is said to be "ab- 
solutely general; it applies to all things and all properties, and it is 
quite self-evident." Moreover, it is a priori: "Since it does not 
mention any particular thing, or even any particular quality or 
relation, it is wholly independent of the accidental facts of the 
existent world, and can be known, theoretically, without any 
experience of particular things or their qualities and relations." 
This conclusion follows from its being laid down as a logical truth 
that "General truths cannot be inferred from particular truths 
alone, but must, if they are to be known, be either self-evident, or 
inferred from premises of which one at least is a general truth. 
But all empirical evidence is of particular truths. Hence if there 
is any knowledge of general truths at all there must be some 
knowledge of general truths which is independent of empirical 
evidence, i.e., does not depend upon sense-data." 

In the latter passage there is not only an implicit but an explicit 
identification of ultimate ("primitive") existential propositions 
with atomic propositions. If empirical (here employed in the 
sense of existential) propositions are atomic, then it certainly fol- 
lows that any propositions about the logical forms by which they 
are related to one another must be supra- and extra- empirical, or 
a priori. They must be known by some kind of rational intuition, 
a conception involved, although in a somewhat disguised way, in 
calling them "self-evident." The apodosis clause of the above 
if-then proposition follows with such neat necessity from the 
protasis clause that it invites attention to the latter. If the ante- 
cedent clause is invalid, the validity of the consequent clause is 
indeterminate, while if the consequent clause is false or doubtful, 
then so is that of the antecedent clause. In other words, the 
passage quoted sets forth a problem. The very necessity of the 
relation of the two clauses merely accentuates the importance of 
the problem. I shall not repeat here the reasons previously given 

6 Bertrand Russell, Scientific Method in Philosophy, and further quotations, 
p. 42, and pp. 56-7. 



156 THE STRUCTURE OF INQUIRY 

for rejecting the clause which postulates atomic existential proposi- 
tions as primitive in independence of their function in inquiry, 
Nor shall I rehearse the reasons for doubting the existence of a 
faculty of pure reason independent of any and all experience, a 
faculty gifted with the power of infallible intuition. 7 

The points directly relevant to the problem are, first, that what 
is "self-evident" in the general logical proposition cited, is its 
meaning. To say that it is self-evident means that one who re- 
flects upon it in the meaning system of which it is a member will 
apprehend its meaning in that relation — exactly as one might ap- 
prehend the meaning, say, of the empirical proposition "that rib- 
bon is blue." The question of the logical force and function of 
the proposition, of the interpretation to be given it, remains open 
— just as does the truth of the empirical proposition after its 
meaning is grasped. 

Secondly, the theoretical interpretation of the significance of 
the meaning directly apprehended is far from self-evident. There 
is, for example, the alternative represented by the theoretical 
position which was stated by Peirce, to the effect that all proposi- 
tions about logical forms and relations are leading principles, not 
premises. They are, from this point of view, formulations of 
operations, which (a) are hypotheses about operations to be per- 
formed in all inquiries which lead to warranted conclusions; and 
(b) are hypotheses that have been confirmed without exception in 
all cases which have led to stable assertions; while (c) failure to 
observe the conditions set forth have been found, as a matter of 
experience of inquiries and their results, to lead to unstable con- 
clusions. 

Such propositions about logical forms as are exemplified in the 
dictum about possession of properties that arc "independent" of 
the specific subject-matter of existential propositions are not (it is 
admitted) conclusions drawn merely from subject-matters as 
purely particular, and they are not proved by these particular 
propositions. But there is nothing in this admission inconsistent 

7 Attention may, however, be called to the fact that the assumption of both 
atomic existential propositions and of rationally intuited truths destroys the 
autonomy of logical theory, rendering it dependent upon psychological and 
epistemological considerations declared by definition to be outside the province 
of logic. 



IMMEDIATE KNOWLEDGE 157 

with their being drawn from operations of inquiry as existential 
and empirical occurrences. In the degree in which we understand 
what is done in inquiries that result in warranted assertions, we 
understand the operational conditions which have to be observed. 
These conditions, when formulated, are the content of general 
propositions about logical forms. The conditions of the required 
operations (required in order that a certain kind of consequence 
may issue) are as much matters of experience as are factual con- 
tents: which are themselves also discriminated in order to serve as 
conditions of a warranted outcome. 

It is not claimed that this proposition about logical propositions 
is "self-evident" as to its truth. It is claimed that it has an intel- 
ligible meaning, capable of being directly grasped as a meaning, 
and that this meaning, when it is used or applied to the problems 
of logical theory serves to clarify and resolve them. The con- 
ception, on the other hand, that "experience" is reducible to im- 
mediately given atomic propositions, that are possessed of self- 
evident truth, introduces complications and confusions. Universal 
propositions about logical forms are propositional functions and as 
such are in themselves neither true nor false. They state modes of 
procedure in inquiry which are postulated as applicable and as 
required in any controlled inquiry. Like mathematical axioms, 
their meaning, or force, is determined and tested by what follows 
from their operative use. 

As far as the doctrine of immediate knowledge is directly con- 
cerned, the discussion has reached an end. But there are certain 
things which may be added from the side of the mediated character 
of all knowledge in order to guard against misapprehension, (a) 
It is not held that inferred interpretations are tested, confirmed, 
verified (or the opposite) by particular objects in their particu- 
larity. On the contrary, it is the capacity of the inferred idea 
to order and organize particulars into a coherent whole that is the 
criterion, (b) It is not held that inference by itself exhausts 
logical functions and determines exclusively all logical forms. On 
the contrary, proof, in the sense of test, is an equally important 
function. 

Moreover, inference, even in its connection with test, is not 
logically final and complete. The heart of the entire theory 



158 THE STRUCTURE OF INQUIRY 

developed in this work is that the resolution of an indeterminate 
situation is the end, in the sense in which "end" means end-k-vie<w 
and in the sense in which it means close. Upon this view, inference 
is subordinate although indispensable. It is not as, it is for example, 
in the logic of John Stuart Mill, exhaustive and all-inclusive. It is 
a necessary but not a sufficient condition of warranted assertions. 



CHAPTER IX 

JUDGMENTS OF PRACTICE: EVALUATION 



^he previous chapter was devoted to enforcing the necessity 
of mediation in knowledge as warranted assertion. This 

. necessity does not stand alone, for it is a necessary phase of 
the theory of inquiry and judgment that has been developed. It 
received separate development because of the traditional and still 
current doctrine of self-evident truths and self -grounded proposi- 
tions. There is, however, another phase of our basic theory which 
stands equally (and possibly to a greater degree) in opposition to 
accepted logical theory, and which accordingly stands also in 
need of explicit treatment. For, contrary to current doctrine, the 
position here taken is that inquiry effects existential transforma- 
tion and reconstruction of the material with which it deals; the 
result of the transformation, when it is grounded, being conversion 
of an indeterminate problematic situation into a determinate re- 
solved one. 

This emphasis upon requalification of antecedent existential 
material, and upon judgment as the resulting transformation, stands 
in sharp contrast with traditional theory. The latter holds that 
such modifications as may occur in even the best controlled inquiry 
are confined to states and processes of the knower — the one con- 
ducting the inquiry. They may, therefore, properly be called 
"subjective," mental or psychological, or by some similar name. 
They are without objective standing, and hence lack logical force 
and meaning. The position that is here taken is to the contrary 
effect: namely, that beliefs and mental states of the inquirer cannot 
be legitimately changed except as existential operations, rooted 
ultimately in organic activities, modify and requalify objective 
matter. Otherwise, "mental" changes are not only merely mental 

159 



160 THE STRUCTURE OF INQUIRY 

(as the traditional theory holds) but are arbitrary and on the road 
to fantasy and delusion. 

The traditional theory in both its empiricistic and rationalistic 
forms amounts to holding that all propositions are purely de- 
claratory or enunciative of what antecedently exists or subsists, 
and that this declarative office is complete and final in itself. The 
position here taken holds, on the contrary, that declarative proposi- 
tions, whether of facts or of conceptions (principles and laws) are 
intermediary means or instruments (respectively material and 
procedural) of effecting that controlled transformation of subject- 
matter which is the end-in-view (and final goal) of all declarative 
affirmations and negations. It is not, be it noted, the occurrence 
of purely declarative propositions that is denied. On the contrary, 
as will be shown later in detail, the existence of such propositions, 
setting forth relationships that obtain between factual data on one 
hand and between conceptual subject-matter on the other hand, is 
expressly affirmed. The point at issue concerns not their being 
but their function and interpretation. 

The position may be stated in the following language: All con- 
trolled inquiry and all institution of grounded assertion necessarily 
contains a practical factor; an activity of doing and making which 
reshapes antecedent existential material which sets the problem of 
inquiry. That this view is not assumed ad hoc but represents what 
certainly occurs (or is a vera causa) in at least some cases, will be 
shown by considering some forms of common sense inquiry which 
aim at determining what is to be done in some practical predica- 
ment. 

Inquiries of this type are neither exceptional nor infrequent. 
For the stock and staple of common sense inquiries and judg- 
ments are of this sort. The deliberations of daily life con- 
cern in largest measure questions of what to make or to do. Every 
art and every profession is faced with constantly recurring prob- 
lems of this sort. To put their existence in doubt is equivalent to 
denying that any element of intelligence enters into any form of 
practice; to affirming that all decisions on practical matters are the 
arbitrary products of impulse, caprice, blind habit, or convention. 
Farmer, mechanic, painter, musician, writer, doctor, lawyer, 
merchant, captain of industry, administrator or manager, has 



JUDGMENTS OF PRACTICE: EVALUATION 161 

constantly to inquire what it is better to do next. Unless the de- 
cision reached is arrived at blindly and arbitrarily it is obtained by 
gathering and surveying evidence appraised as to its weight and 
relevancy; and by framing and testing plans of action in their 
capacity as hypotheses: that is, as ideas. 

By description, the situations which evoke deliberation resulting 
in decision, are themselves indeterminate with respect to what 
might and should be done. They require that something should 
be done. But what action is to be taken is just the thing in question. 
The problem of how the uncertain situation should be dealt with 
is urgent. But as merely urgent, it is so emotional as to impede and 
often to frustrate wise decision. The intellectual question is what 
sort of action the situation demands in order that it may receive a 
satisfactory objective reconstruction. This question can be 
answered only, I repeat, by operations of observation, collection of 
data and of inference, which are directed by ideas whose material 
is itself examined through operations of ideational comparison and 
organization. 

I did not include the scientist in the list of persons who have to 
engage in inquiry in order to make judgments upon matters of 
practice. But a slight degree of reflection shows that he has to 
decide what researches to engage in and how to carry them on — a 
problem that involves the issue of what observations to undertake, 
what experiments to carry on, and what lines of reasoning and 
mathematical calculations to pursue. Moreover, he cannot settle 
these questions once and for all. He is continually having to judge 
what it is best to do next in order that his conclusion, no matter 
how abstract or theoretical it may be as a conclusion, shall be 
grounded when it is arrived at. In other words, the conduct of 
scientific inquiry, whether physical or mathematical, is a mode of 
practice; the working scientist is a practitioner above all else, and is 
constantly engaged in making practical judgments: decisions as to 
what to do and what means to employ in doing it. 

The results of deliberation as to what it is better to do are, 
obviously, not identical with the final issue for the sake of which 
the deliberative inquiries are undertaken. For the final issue is 
some new situation in which the difficulties and troubles which 
elicited deliberation are done away with; in which they no longer 



162 THE STRUCTURE OF INQUIRY __ 

exist. This objective end cannot be attained by conjuring with 
mental states. It is an end brought about only by means of 
existential changes. The question for deliberation is what to do 
in order to effect these changes. They are means to the required 
existential reconstruction; a fortiori, the inquiries and decisions 
which issue in performance of these acts are instrumental and inter- 
mediate. But what should be done depends upon the conditions 
that exist in the given situation and hence require a declarative or 
enunciatory proposition: "The actual conditions are so-and-so.'* 
These conditions are the ground of inference to a declarative 
proposition that such and such an act is the one best calculated to 
produce the desired issue under the factual conditions ascertained. 
Declarative propositions as to the state of facts involved set 
forth the obstacles and resources to be overcome and administered 
in reaching the intended goal. They state potentialities, positive 
and adverse. They function as instrumentalities. The proposi- 
tions which set forth the way existing conditions should be dealt 
with stand in functional correlation with the enunciatory proposi- 
tions which state existing conditions. The propositions as to pro- 
cedure are not carriers of existential or factual materials. They are 
of the general form: "If such and such a course is adopted under 
the existing circumstances, such and such will be the probable re- 
sult." Logically, the formation of these hypotheses as to methods 
of action involves reasoning, or a series of declarative propositions 
stating relationships of conceptual materials. For it is only rarely 
that the idea of the procedure which first suggests itself can be 
directly set to work. It has to be developed; this development 
constitutes rational discourse, which in scientific practice usually 
takes the form of mathematical calculation. 

Preliminary to offering illustrations of what has been said, I 
shall summarize formally what is logically involved in every situa- 
tion of deliberation and grounded decision in matters of practice. 
There is an existential situation such that (a) its constituents are 
changing so that in any case something different is going to hap- 
pen in the future; and such that (b) just 'what will exist in the 
future depends in part upon introduction of other existential con- 
ditions interacting with those already existing, while (c) what 
new conditions are brought to bear depends upon what activities 



JUDGMENTS OF PRACTICE: EVALUATION 163 

are undertaken, (d) the latter matter being influenced by the inter- 
vention of inquiry in the way of observation, inference and reason- 
ing. 

The illustration I shall employ to exemplify these four condi- 
tions is that of a person who, being ill, deliberates about the proper 
course to adopt in order to effect recovery. (1) Bodily changes 
are already going on which in any case will have some existential 
issue. (2) It is possible to introduce new conditions that will be 
factors in deciding the issue — the question for deliberation being 
whether they should be introduced and if so, which ones and how. 
(3) Deliberation convinces the one who is ill that he should see a 
physician. A proposition to this effect is equivalent to the con- 
clusion that the consequences of the visit are calculated to intro- 
duce the interacting factors which will yield a desired issue. (4) 
Hence, the proposition when executed actually introduces inter- 
vening conditions which interact with antecedent existing condi- 
tions to modify their course and thus influence the issue. The latter 
is different from what it would have been if inquiry and judgment 
had not intervened — even if recovery of health is not attained. 

Whenever there is genuine deliberation, there are alternatives at 
almost every step of the way. There is something to be said or 
tentatively affirmed at each step on both sides of the questions that 
come up. Reflection on past experience indicates that it is often 
well to let "nature take its course." But is the present case of that 
kind? The question of financial expense may enter in; that of 
whether a competent physician is available or what physician to 
consult; the question of the patient's engagements for the next few 
days and weeks, and the bearing of the physician's advice upon the 
patient's possibility of fulfilling them, etc., etc. 
. Such factual matters as these are examined and formulated in 
propositions. Each state of facts presented in a proposition sug- 
gests its own alternative course of action, and if there is genuine 
inquiry the suggestion has to be formulated. The formulation 
or proposition has then to be developed in terms of the probable 
consequences of adopting it. This development occurs in a series 
of if-then propositions. If the man finally decides to see such and 
such a doctor, the resulting proposition represents, in effect, an 
inference that this mode of procedure stands the better chance of 



164 THE STRUCTURE OF INQUIRY 

introducing those factors which will yield, in their inter-action 
with existing conditions, a desired future existential situation: an 
inference that it will give to factors already in operation a direc- 
tion that they would not take if left to themselves. 

The contents of the propositions framed about matters of fact 
and about alternative courses of action (including the one adopted) 
are neither self-determined nor self-sufficient. They are de- 
termined with reference to an intended future issue and hence are 
instrumental and intermediate. They are not valid in and of them- 
selves, for their validity depends upon the consequences which 
ensue from acting upon them— as far as these consequences ac- 
tually ensue from the operations the propositions dictate and are 
not accidental accretions. Let the factual proposition be repre- 
sented by "I am seriously ill." In the context indicated, the propo- 
sition is without point if taken to be final and complete. Its logical 
force consists in its potential connection with a future situation. 
The declarative proposition "I should or shall see a doctor" is simi- 
larly functional. It formulates the possible operation which, if per- 
formed, will aid in existential production of a future situation dif- 
ferent in quality and significance from that which will exist if the 
indicated action is not taken. The same considerations will be 
found to apply to declarative propositions made by the attending 
physician about the facts which locate and describe the illness on 
the one hand, and the course of action he prescribes for dealing 
with the illness on the other. 

This analysis^ if accepted, carries with it recognition that de- 
clarative propositions (themselves the results of judgments of pro- 
visional appraisal) are factors which enter actively "into the actual 
constitution of the existential subject-matter of the final judgment. 
This final subject-matter may not be that which was hoped for and 
intended. But in any case it is somewhat different from what it 
would have been if the operations, dependent upon intervening 
instrumental propositions, had not taken place. According to the 
commonly accepted interpretation of declarative propositions it 
is a straight contradiction that they should enter into the ultimate 
structure of the very situation they are "about." But the con- 
tradiction results from the theory which is accepted, not from 
the propositions themselves; it is a consequence of ignoring the 



JUDGMENTS OF PRACTICE: EVALUATION 165 



intermediary and operational force of the propositions that are 
formed. 

The standard account of the example discussed on the basis of 
traditional theory would be somewhat as follows: The proposi- 
tions "I am ill" and "When one is ill, one should consult a doc- 
tor" are taken respectively as the minor and major premises of a 
syllogism from which the conclusion "I should see a doctor" nec- 
essarily follows. This interpretation rests upon taking advantage 
of an ambiguity. It may be but a linguistic rendering of a genu- 
ine judgment already made. In this case, the analysis of the text 
is confirmed. For then both major and minor state decisions 
reached in inquiry as to what the state of affairs should be in 
order to modify them in a given direction. Taken literally, how- 
ever, the interpretation means that there was no inquiry and no 
judgment. It only means that the person in question, whenever he 
fancies he is ill has the habit of going automatically to a physician. 
There is no element of doubt or indeterminateness, no inquiry and 
no forming of propositions. There is a direct stimulus and it is re- 
sponded to in accord with a previously formed habit. The alleged 
syllogism is but an externally imposed account of what has taken 
place in action in which no logical forms are involved. 

This situation is of significance because it brings out by con- 
trast the situations in which judgment does occur. A man may 
have a regular habit of consulting physicians because he is vale- 
tudinarian and on that account does not exercise judgment. Or 
he may have the tendency to go whenever his symptoms are se- 
vere and yet on this particular occasion be in doubt whether he is 
sufficiently ill to justify going. Then he engages in reflection. 
Moreover, in the concrete a man does not decide to see a doctor; 
he decides to see some given doctor, and he may need to investi- 
gate what physician to see. He may have reasons for thinking his 
financial state renders it better to take a chance about getting well, 
etc. The account which reduces a proposition of practice to a 
formal combination of a singular and a general proposition thus 
applies only to ex post -facto linguistic analyses of either an act 
performed from habit without the intermediation of judgment 
or else of a judgment that has been completed. If deliberation and 
appraisals involving propositions actually intervene in reaching the 



166 THE STRUCTURE OF INQUIRY _^ 

decision "I shall see a physician," then a judgment of practice is a 
factor in the ultimate determination of the existential material 
which the preliminary judgments of appraisal are about. 

The particular instance chosen can hardly be supposed to settle 
the larger question at issue. This problem is so important that I 
shall continue its discussion through a series of instances. 

1. There are cases in which judgments of practice have to de- 
termine what to do next, "right away," in order to produce a spe- 
cific existential situation as the result of the activity the judgment 
prescribes. One notes, for example, a motor car bearing down 
upon him. He may automatically swerve. In this case, there 
is no judgment and no proposition. But the situation may be such 
as to evoke deliberation. In this case, there will be observation 
of existing conditions (locating the problem) and formation of a 
plan of action to meet the emergency (solve the problem). The 
decisions made by an umpire in the course of a game afford an 
even better illustration. He has to form propositions about ob- 
served facts and about the rule that is applicable to their inter- 
pretation. Both his estimate of facts and of the rule that is ap- 
plicable may be questioned, but in any case the final judgment of 
"Safe" or "Out" enters as a determining factor in the subsequent 
existential course of events. This fact shows that the action and 
position of, say, a runner in a baseball game are not that which 
is judged. The object of judgment is the total situation in which 
action occurs. Propositions about just what a batter or runner has 
done and about the rule (conception) which is applicable, are 
intermediate and instrumental, not final and complete. 

The two instances cited illustrate what is meant by the phrase 
"procedural means" applied to the predicate of judgment. The 
subject-matter of the predicate represents an end-in- view, which 
is an anticipation of an existential consequence, an end in the 
sense of a fulfilling close and termination. The end-iii-view of 
the man who sees an automobile approaching him is getting to a 
place of safety, not safety itself. The latter (or its opposite) is 
the end in the sense of close. Unless the anticipation or end-in- 
view is an idle fantasy, it takes the form of an operation to be 
performed. Similarly, the proposition "Out" or "Safe" in the 
case of the runner in the game is operational in that it decides 



JUDGMENTS OF PRACTICE: EVALUATION 167 

what the runner shall then proceed to do and how the game shall 
go on. If the existential end in the sense of final outcome or close, 
were a term in a proposition, it would be taken to be already com- 
pleted. Only if the end figures as a directive means to perform 
the action by which the actual termination is brought about is it 
other than self-defeating. 

The predicate is not a "realistic" apprehension and enunciation 
of something already in existence; it is an estimate, based on real- 
istic observation of facts as conditions of possible issues, of some- 
thing to do. Likewise, the ideas of a goal for a runner in a race 
or of a target for an archer are obstructive not helpful unless they 
are translations of the final mark as an existence into means 
whereby — procedural means. The runner employs the thought of 
the goal as means of regulating his pace, etc., at different stages 
of his running; the archer uses the thought of the target, in con- 
nection with observations of the direction and force of wind, 
etc., as a guide or direction in taking aim. The difference between 
the two senses of end, namely, end-in-view and end as objective 
termination and completion, is striking proof of the fact that in 
inquiry the termination is not just realistically apprehended and 
enunciated but is stated as a way of procedure. Confusion of the 
two senses of "end" is the source of the notion that a judgment 
of practice is either purely declarative or else is so merely practical 
that it has no logical status. 

2. Moral evaluations are also a case in point. The common, per- 
haps prevailing, assumption is that there are objects which are 
ends-in-themselves; that these ends are arranged in a hierarchy 
from the less to the more ultimate and have corresponding au- 
thority over conduct. It follows from this view that moral "judg- 
ment" consists simply in direct apprehension of an end-in-itself in 
its proper place in the scheme of fixed values. It is assumed that 
apart from this hierarchy of fixed ends, a moral agent has no al- 
ternative save to follow his desires as they come and go. Accord- 
ing to the position here taken, ends as objective termini or as 
fulfilments function in judgment as representative of modes of 
operation that will resolve the doubtful situation which evokes 
and demands judgment. As ends-in-vie*w they denote plans of 
action or purposes. The business of inquiry is to determine that 



168 THE STRUCTURE OF INQUIRY 

mode of operation which will resolve the predicament in which the 
agent finds himself involved, in correspondence with the observa- 
tions which determine just what the facts of the predicament are. 

The notion that a moral judgment merely apprehends and 
enunciates some predetermined end-in-itself is, in fact, but a way 
of denying the need for and existence of genuine moral judgments. 
For according to this notion there is no situation which is problem- 
atic. There is only a person who is in a state of subjective moral 
uncertainty or ignorance. His business, in that case, is not to 
judge the objective situation in order to determine what course of 
action is required in order that it may be transformed into one that 
is morally satisfactory and right, but simply to come into intel- 
lectual possession of a predetermined end-in-itself. Goods pre- 
viously experienced assuredly are material means of reaching a judg- 
ment as to what to do. But they are means, not fixed ends. They 
are material to be surveyed and evaluated in reference to the kind of 
action needed in the existing situation. 

The position which holds that moral judgment is concerned 
with an objective unsettled situation and that ends-in-view are 
framed in and by judgment as methods of resolving operations is 
consistent with the fact that, because of recurrence of similar situ- 
ations, generic ends-in-view, as ways of acting, are built up and 
have a certain prima facie claim to recognition in new situations. 
But these standardized "prepared" propositions are not final; though 
highly valuable means, they are still means for examining the ex- 
isting situation and appraising what mode of action it demands. 
The question of their applicability in the new situation, their 
relevancy and weight with respect to it, may and often does lead to 
their being re-appraised and re-framed. 

3. Interrogative Propositions. Whether questions are proposi- 
tions in any logical sense is not a matter often discussed. Logi- 
cians who do raise the problem usually take the position that they 
are not genuine propositions. Upon the position here taken, all 
propositions as distinct from judgment have an interrogative as- 
pect. Since they are provisional, they are not only subject to 
being questioned but they themselves raise questions of pertinency, 
weight and applicability. When either facts or conceptions are 
taken to be completely assured (whether because of earlier sue- 



JUDGMENTS OF PRACTICE: EVALUATION 169 

cessful use or for any other reason), direct action, not judgment, 
ensues. It is a matter of great practical convenience that many- 
facts and ideas may be so taken and directly used. But conver- 
sion of this practical value into assured logical status is one of the 
commonest ways of establishing the dogmatism which is the great 
enemy of free and continued inquiry. 

Bosanquet is one of the comparatively few writers who has 
dealt expressly with the logical status of interrogations. He says 
they are only tentative and that "a tentative judgment lacks the 
diif erentia of judgment. It does not assert; it does not claim truth; 
a question as such cannot be an object of thought as such ... it 
is not an attitude which the intellect can maintain within itself. 
... It is a demand for information; its essence is to be directed 
to a moral agent in which it may produce action." 2 

The passage quoted involves a point previously discussed, 
namely, the double character of judgment as provisional appraisal 
or estimate and as conclusive or final. What Bosanquet said evi- 
dently applies to judgment in its latter capacity. In ruling out from 
the meaning of judgment all preliminary estimates and evaluations 
concerning the force and relevancy of facts and ideas, his view 
leads to the conclusion he draws; namely, that inquiry is not a 
form of judgment and therefore as such is not logical in status. 
This position is of crucial significance in its far-reaching implica- 
tions. 

It is surely not unscientific to regard the actual work of science 
as one of inquiry. A position which rules science out of the 
field and scope of logic, save as a body of propositions that are 
accepted independently of the methods of inquiry by which they 
are reached, is with equal certainty not one to be lightly accepted. 
Ordinary language uses the expression "the matter in question" 
as a synonym for the subject-matter with which inquiry is oc- 
cupied. From the standpoint of both science and common sense, 
it would seem more correct to say that a question (in the sense of a 
questionable and questioned subject-matter) is the object of 
"thought," than to say, with Mr. Bosanquet, that "a question can- 
not be the object of thought." 

That a question is a demand for action on someone's part is 

1 logic, Vol. I, p. 35. 



170 THE STRUCTURE OF INQUIRY 

a statement which, taken in isolation, is in full agreement with the 
position of this work. Judgment as appraisal may enter even 
into the formation of questions addressed to another person, since 
just the question which should be asked is far from being a self- 
evident matter. Nevertheless, the statement that a question by its 
nature is something addressed to another person, ignores the 
basic fact that questions are addressed to existential subject-mat- 
ter. A scientific inquiry may be regarded as a request "for in- 
formation." But the needed information is not handed out ready- 
made by nature. It requires judgment to decide what questions 
should be asked of nature, since it is an affair of formulating the 
best methods of observation, experimentation and conceptual in- 
terpretation. 

The last statement brings our discussion face to face with the 
problem concerning the relation of inquiry to judgments of prac- 
tice. For determination of what questions to ask and how to ask 
them is an affair of judging what should be done in order to se- 
cure the material, factual and conceptual, which is necessary and 
sufficient to resolve an unsettled situation. One has only to bring 
to mind the procedure of a lawyer or a physician in any given case, 
to see how fundamentally his problem is one of framing right 
questions — the criterion of "rightness" being capacity to bring 
out the material which is relevant and effective in settling the 
situation that evokes inquiry. 

4. Deliberation is involved in all the instances considered. But 
one aspect of deliberation, in its emphatic sense, is so important 
that it is advisable to treat the topic in a separate heading. Gen- 
uine deliberation proceeds by institution and examination of al- 
ternative courses of activity and consideration of their respective 
consequences. This fact throws light upon the functional nature 
of disjunctive and hypothetical propositions. Taxonomic systems, 
such as are exemplified in botany and zoology, are large scale 
examples of disjunctive propositions. They were once regarded 
as marking the final goal of science — a view that followed con- 
sistently from the classic conception of fixed species. They are 
now treated as useful means for the conduct of inquiry and of 
value only in this function; for any given taxonomic system is 
treated as flexible and subject to constant revision. But unfor- 



JUDGMENTS OF PRACTICE: EVALUATION 171 

tunately, logical texts are given to treating disjunctive propositions 
as a separate theme. Consequently they employ, as illustrative 
material, disjunctions established by prior inquiry without refer- 
ence to the inquiries by which they are established and without 
reference to those in which they further operate; while in the 
actual work of science taxonomic disjunctions are so regularly 
treated as purely instrumental devices as to lose all independent 
standing. It would hardly be an exaggeration to say that em- 
phatic regard for taxonomy exposes a given scientific worker to 
something approaching contempt on the part of scientific workers 
in more advanced fields. 

Disjunctive propositions are connected with practical judgment, 
for deliberation upon matters of policy requires (a) that alter- 
native possibilities be instituted and explored, and (b) that they 
be such as to be readily comparable with one another. For ex- 
ample, a man who has come into possession of a large sum of 
money proceeds to deliberate as to what he shall do with it. His 
deliberation gets nowhere unless it takes the form of setting up 
alternative possible uses for the funds at command. Shall it be 
placed in a savings bank to draw interest? Invested in stocks, in 
bonds, in real estate? Or shall it be used for purposes of travel, 
or to buy books, apparatus, etc.? The problematic situation is 
made relatively determinate by analysis into alternatives, each of 
which is represented in a disjunctive proposition as a member of a 
system. 

In the example given it is clear that each proposition is formed 
as a means of determining what to do, and that the resulting de- 
termination is a means of bringing into existence a certain eventual 
situation. Experts in special fields soon establish a set of alterna- 
tives. For new cases these alternatives are prepared materials, just 
as an artisan has at hand a set of tools relevant to his line of 
activity. In such cases, judgment goes rather to the question which 
one of the disjunctive set to employ rather than to formation of 
disjunctive propositions. But, nevertheless, the latter remain in- 
struments. Hypostization of instruments into something final and 
complete places a restriction on further inquiry. For it subjects 
the conclusion to be reached to a preconception which is as- 
sumed to be beyond question and examination. 



172 THE STRUCTURE OF INQUIRY 

The relation of hypothetical to disjunctive propositions needs 
only to be suggested at this point. The meaning of each alterna- 
tive mode of action is constructed in terms of the consequences 
which acting upon it will produce. The development of this 
meaning takes place through reasoning in the form "If such an 
alternative be adopted, then such and such and such consequences 
may be expected to follow." The derived consequences, com- 
pared with the consequences of other hypothetical propositions, 
provide the ground for tentative acceptance or rejection. In 
actual practice, the development of if-then propositions of this 
sort is often not carried far. But from the standpoint of war- 
ranted final judgment as to what should be done, disjunctives 
should be exhaustive, and development of each disjunctive mem- 
ber of the system, as a hypothesis, should be thorough. 

5. Evaluation. A standing ambiguity in the word value, both 
as verb and noun, has frequently been pointed out. In one of its 
meanings "to value" is to enjoy and the resulting enjoyment is 
figuratively called a value. There is neither reflection nor inquiry 
in these cases of enjoyment as far as they occur spontaneously. 
The fact of an enjoyment may, however, be recorded and com- 
municated linguistically. The resulting linguistic expression will 
have the outward form of a proposition. But unless a question has 
arisen it is a social communication rather than a proposition, unless 
the communication is made to provide a datum in resolving a new 
situation. If, however, the question is raised whether the subject- 
matter is worthy of being directly enjoyed; if, that is, the question 
is raised as to the existence of adequate grounds for the enjoy- 
ment, then there is a problematic situation involving inquiry and 
judgment. On such occasions to value means to weigh, appraise, 
estimate: to evaluate — a distinctly intellectual operation. Reasons 
and grounds one way and the other have to be sought for and 
formulated. 

That such situations arise regarding persons once loved and 
admired, regarding objects upon which esteem (as distinct from 
estimation) was once lavished, is as indisputable as it is significant 
for the point at issue. For their occurrence shows that we evaluate 
only when a value, in the sense of material enjoyed, has become 
problematic. The propositions in this case are of a very different 



JUDGMENTS OF PRACTICE: EVALUATION 173 

logical order from verbally similar sentences which only record 
and communicate the fact that a certain enjoyment, admiration or 
esteem has actually taken place. The latter "propositions' ' in- 
deed record an occurrence, but if they have any logical status it is 
when they are material of an investigation conducted to reach a de- 
cision whether they were justified when they were enjoyed, or 
are justifiable in the present situation. Should we now commit 
ourselves to such an attitude? If we do, may we not regret it later? 

Such questions arise in a wide range and variety of cases, from 
cases of eating a food which one knows from past experience will 
be immediately enjoyed, to serious moral predicaments. The only 
way of answering the questions, of resolving the doubts that have 
arisen, is to review the existential consequences which will prob- 
ably occur if esteem, admiration, enjoyment are engaged in. For 
attitudes, esteem, etc., are active attitudes; they are ways of act- 
ing which produce consequences, and consequences can be ground- 
edly anticipated only as consequences of conditions that are 
operative. The fact of enjoyment is only one of the operative 
conditions. It produces consequences — as in the act of eating 
the immediately enjoyed food — only through interaction with 
other existential conditions. The latter must, therefore, be in- 
dependently surveyed. There is no way to estimate their probable 
consequences save in terms of what has happened in similar cases 
in the past, either one's personal past or in the recorded experience 
of others. On their bare face, existing conditions do not tell what 
their consequences will be. We have to investigate connections 
— usually that of cause-effect. Connections are then formulated 
in abstract generalized conceptual propositions, in rules, princi- 
ples, laws. But the question of the applicability of the rules and 
principles at hand (however tested they have been) to the special 
situation in question always enters in. Choice has to be made 
among them. Consequently, in order to obtain a grounded final 
judgment there also has to be evaluation or appraisal of principles. 

An evaluative proposition is not, then, merely declarative with 
respect either to facts or to conceptual subject-matter. The facts 
may be undoubted; I certainly have enjoyed this object in the 
past; I will get immediate enjoyment from it now. Certain gen- 
eral principles may be accepted as standards. But neither the 



174 THE STRUCTURE OF INQUIRY 

facts nor the standardized rules as they present themselves are 
necessarily decisive in the evaluation being made. They are, 
respectively, material and procedural means. Their relevancy and 
weight in the present situation is the matter to be determined by 
inquiry before an evaluative appraisal can be grounded. 

Such evaluative judgments are clearly an instance of judgments 
of practice; or, more strictly, all judgments of practice are evalua- 
tions, being occupied with judging what to do on the basis of 
estimated consequences of conditions which, since they are existen- 
tial, are going to operate in any case. The more it is emphasized 
that direct enjoyment, liking, admiration, etc., are themselves 
emotional-motor in nature, the clearer is it that they are modes of 
action (of interaction). Hence a decision whether to engage 
or indulge in them in a given situation is a judgment of practice — 
of what should be done. 

A point still more important for logical theory is that these 
evaluative judgments (as was brought out in the earlier discus- 
sion of judgment) enter into the formation of all final judgments. 
There is no inquiry that does not involve judgments of practice. 
The scientific worker has continually to appraise the information 
he gathers from his own observations and from the findings of 
others; he has to appraise its bearing upon what problems to under- 
take and what activities of observation, experimentation and cal- 
culation to carry out. While he "knows," in the sense of under- 
standing, systems of conceptual materials, including laws, he has to 
estimate their relevancy and force as conditions of the particular 
inquiry undertaken. Probably the greatest source of the relative 
futility—or at least infertility — of that part of many logical texts 
which deal with scientific method, is failure to relate the material 
which they expound to the operations by which they are reached 
and the further operations they suggest, indicate and serve to direct. 

6. Appreciation. The fact has been emphasized that a judg- 
ment of value is not identical with a statement that such and such 
a person arouses admiration and liking or that such and such an 
event or object was or is enjoyed. Such "propositions" have the 
property of truth only in a moral sense; that is, in opposition to 
being deliberate lies. Such propositions may, however, become 
constituents of a judgment of value, or an evaluation. They 



JUDGMENTS OF PRACTICE: EVALUATION 175 

take on this status when they are employed as material means of 
determining whether a given person or action should be admired 
or a given object enjoyed. When the statement "I like this pic- 
ture" is changed into the proposition "This picture is beautiful," 
the issue shifts to the picture as object. To be valid, the latter 
proposition must be grounded upon discernible and verifiable 
qualities of the picture as an object. It depends, on one hand, 
upon discrimination of observable qualities and, on the other, 
upon the conceptual meanings which constitute, when they are 
made explicit, the definition of beauty. These statements are so 
far from being inconsistent with the existence of immediate non- 
judgmental esthetic experience that esthetic judgment must, to be 
genuine, grow out of the latter. But the immediate experience is 
not expressed in the statement "I like it." Its natural expression 
is rather the attitude of the observer or an interjection. 

The last remarks bear upon the topic of appreciation. It is not 
bare enjoyment but enjoyment as consummation of previous proc- 
esses and responses that constitutes appreciation. These previous 
states and operations involve reflective observation that partakes of 
the nature of analysis and synthesis, of discrimination and inte- 
gration of relations. Appreciation, if genuine, is toward a subject- 
matter that is representative. It is not representative of something 
outside the appreciated object. The object in question is repre- 
sentative of that which has led up to it as fulfilment or consum- 
matory close. Appreciation thus differs in a fundamental way 
from casual enjoyments that are just hit upon or let drop. 

Words such as climax, peak, culmination, refer to consummatory 
objects. Any object or event that can be called by such names 
has an intrinsic reference to what went before. The words in- 
dicate that what preceded did not merely occur before the time 
of the peak but that they were such as to have the climacteric 
outcome as their own issue. Wherever there is appreciation there 
is the heightened quality produced by intrinsic connection of the 
object appreciated with its casual conditions. Its opposite is not 
dis-like or dis-enjoyment but de-preciation — disparagement of a 
result or product in its connection with the conditions and efforts 
of which it is the fruit. A man may take a drink of water almost 
automatically to quench thirst. If he is journeying in a barren 



176 THE STRUCTURE OF INQUIRY 

land and forms an estimate of where he may find water and upon 
going to the spot quenches his thirst, he has a heightened quality 
of experience. Water is appreciated as he does not appreciate it 
when all he has to do is to turn a faucet and hold a tumbler under 
the stream that flows out. His experience has the representative 
quality of being an eventuation, a consummation. 

There is, accordingly, an element of evaluation involved in 
appreciation. For such objects are not ends in the sense of being 
merely termini, but in the sense of being fulfilments: satisfactions 
in the literal sense in which that word means "inaking jwf-ficient" 
something &-ficient. Consequently, judgments of appreciation 
are found wherever subject-matter undergoes such development 
and reconstruction as to result in a satisfying complete whole. 
Consider the following quotation as an illustrative of this point: 
"Classical thermo-dynamics form a self-consistent and very ele- 
gant theory, and one might be inclined to think that no modifica- 
tion of it would be possible which did not introduce arbitrary 
features and completely spoil its beauty. This is not so since 
quantum mechanics has now reached a form in which it can be 
based on general laws, and is, although not yet quite complete, 
even more elegant and pleasing than the classic theory in the 
problems with which it deals." * 

The words beauty, elegance, show clearly that here is a case of 
appreciation. Even slight analysis of the passage shows that the 
theory is elegant and has beauty because its subject-matter presents 
a consummated harmonious ordering of diverse facts and concep- 
tions. Intellectual activity, science, has its phases of appreciation 
as truly as have the fine arts. They arise whenever inquiry has 
reached a close that fulfils the activities and conditions which led 
up to it. Without these phases, sometimes intense, no inquirer 
would have the experiential sign that his inquiry had reached its 
close. 

Judgments of appreciation are not confined, however, to the 
final close. Every complex inquiry is marked by a series of stages 
that are relative completions. For complex inquiries involve a 
constellation of sub-problems, and the solution of each of them is a 
resolution of some tension. Each such solution is a heightening of 

# Dirac, Quantum Mechanics, p, 1. 



JUDGMENTS OF PRACTICE: EVALUATION 177 

subject-matter, in direct ratio to the number and variety of dis- 
crepant and conflicting conditions that are brought to unification. 
The occurrence of these judgments of completion, not different in 
kind from those ordinarily called esthetic, constitutes a series of 
landmarks in the progress of any undertaking. They are signs of 
the achieved coherence of factual material and the consistency of 
conceptual material. They are indeed so important in their func- 
tion of being clews and giving direction that the sense of harmony 
which attends them is too readily taken as evidence of truth of the 
subject-matter involved. 2 This error is due to isolating the feeling 
of harmony and congruity from the operations by which discrep- 
ant material is brought into harmonious union. The immediate 
experience of congruity, which is a valuable guide in conduct of 
inquiry, is converted into a criterion of objective truth. 

This hypostization has affected the three most generalized forms 
of appreciation and produced the concepts of the Good, the True 
and the Beautiful as ontological absolutes. The actual basis of 
these absolutes is appreciation of concrete consummatory ends. 
In the case of intellectual, esthetic and moral experiences, the ob- 
jective completion of certain unsettled existential conditions is 
brought about with such integrity that the final situation is pos- 
sessed of peculiar excellence. There is the judgment "This is 
true, beautiful, good" in an emphatic sense. Generalizations are 
finally framed on the ground of a number of such concrete reali- 
zations. Being true, beautiful, or good, is recognized as a common 
character of subject-matters in spite of great differences in their 
actual constituents. They have, however, no meaning save as 
they indicate that certain subject-matters are outstanding consum- 
matory completions of certain types of previously indeterminate 
situations by means of the execution of appropriate operations. 
Good, true, beautiful, are, in other words, abstract nouns desig- 
nating characters which belong to three kinds of actually attained 
ends in their consummatory capacity. 

Classic theory transformed ends attained into ends-in-themselves. 
It did so by ignoring the concrete conditions and operations by 
means of which the fulfilments in question are brought about. 

2 Cf. what was said in Chap. V about the esthetic nature of standards in Greek 
science, pp. 84, 96. 



178 THE STRUCTURE OF INQUIRY 

The traits which marked subject-matters in virtue of their being 
successful resolutions of problems of intellectual inquiry, of artis- 
tic construction and of moral conduct, were isolated from the con- 
ditions which gave them their standing and significance. Being 
thus isolated, they were necessarily hypostatized. In isolation 
from the means by which consequences are reached, they were 
taken to be the external ideals and standards of the very opera- 
tions of inquiry, artistic creation and moral endeavor, of which 
in fact they are generalized results. This hypostization always 
happens when concrete ends in their terminal nature are erected 
into "ends-in-themselves." 

The generalized and abstract conceptions of truth, beauty and 
goodness have a genuine value for inquiry, creation and conduct. 
They have, like all genuine ideals, a limiting and directive force. 
But in order to exercise their genuine function they must be taken 
as reminders of the concrete conditions and operations that have 
to be satisfied in actual cases. In serving as such generalized in- 
struments, their meaning is exemplified in their further use, while 
is also clarified and modified in this use. The abstract meaning of 
truth, of being true, for example, has changed with development 
of the methods of experimental inquiry. 

In conclusion, the paradox that seems to attend the conception 
of judgments of practice which has been presented, will be re- 
curred to. Irrespective of the question of paradox, there are but 
two alternatives regarding the intellectual status of deliberation: 
Either the intermediate and tentative propositions formed during 
the course of deliberation must be admitted to exercise a deter- 
mining influence upon the very subject-matter they are about, or 
else all intellectual standing and bearing must be denied to them. 
The apparent paradox enters if the first interpretation is adopted. 
The idea is paradoxical, moreover, only from the standpoint of a 
prior conception of the nature of propositions: viz., that they are 
purely declaratory and are final and complete in this declaratory 
capacity. The problem takes on a very different aspect if it be 
admitted, even as a hypothesis, that what they declare is the need 
and advisability of performing certain operations as means of at- 
taining a final subject-matter which may be groundedly asserted. 
For upon this basis, the idea that propositions are factors in deter- 



JUDGMENTS OF PRACTICE: EVALUATION 179 

mining the very subject-matter they are about is exactly what is 
to be expected instead of being paradoxical. 

The issue will perhaps be clarified if we note in this connec- 
tion that a certain ambiguity is attached to the word about. On 
the one hand, a proposition is said to be about something which 
does not appear as a term in the proposition. On the other, it is 
said to be about one of the terms of the proposition, usually about 
that term which is the grammatical subject of the sentence which 
expresses the affirmation or denial in question. For example, a 
man inquires into the subject-matter which relates to some per- 
plexing question of foreign relations — his inquiry as a whole is 
about the perplexing situation. In the course of the inquiry, he 
makes propositions about states of fact and about rules of inter- 
national law; the facts and rules are explicit constituents of the 
propositions. But these propositions are about (or refer to) sub- 
ject-matters which are not a constituent of any of the propositions. 
Their point and force lies in that which they are about, the sit- 
uation they serve to determine, and a situation that does not appear 
as a term in any proposition. 

The net conclusion is that evaluations as judgments of practice 
are not a particular kind of judgment in the sense that they can be 
put over against other kinds, but are an inherent phase of judg- 
ment itself. In some cases, the immediate problem may so directly 
concern appraisal of existences in their capacity as means, positive- 
negative (resources and obstacles), and so directly concern ap- 
praisal of the relative importance of possible consequences that 
offer themselves as ends-in-view, that the evaluative aspect is the 
dominant one. In that case, there are judgments which in a rel- 
ative sense may be called valuational in distinction from the sub- 
ject-matter of other judgments where this aspect is subordinate. 
But since selection of existences to serve as subject-data and of 
ideas to serve as predicate-possibilities (or ends in view) is neces- 
sarily involved in every judgment, the valuation operation is in- 
herent in judgment as such. The more problematic the situation 
and the more thorough the inquiry that has to be engaged in, 
the more explicit becomes the valuational phase. The identity of 
valuational judgment with judgments of practice is implicitly 
recognized in scientific inquiry in the necessity of experiment for 



180 THE STRUCTURE OF INQUIRY 

determination of data and for the use of ideas and conceptions— 
including principles and laws— as directive hypotheses. In sub- 
stance, the present chapter is then a plea that logical theory be 
made to conform with the realities of scientific practice, since in 
the latter there are no grounded determinations without operations 
of doing and making. 



CHAPTER X 

AFFIRMATION AND NEGATION: 

JUDGMENT AS REQUALIFICATION 



-nJHERE is a contrast between the traditional theory of positive 
and negative propositions and what occurs in the conduct 

. of inquiry. The contrast invites examination. In scientific 
inquiry there is scrupulous attention to exceptions and whatever 
appear to be exceptions. The technique of inquiry is concerned 
as much with effective eliminations as with noting agreements. 
No amount of agreement among the traits of phenomena investi- 
gated suffices of itself to establish a conclusion; agreements have 
to be safeguarded at every point by observation of differences. 
Experimental operations are undertaken with the express object 
of instituting deliberate variations of conditions in order to bring 
out negative traits which serve to test currently accepted con- 
clusions. Should logical theory take its cue for interpretation of 
affirmative and negative propositions from what happens in the 
conduct of inquiry, it would be evident that (1) such propo- 
sitions are functional in resolution of a problematic situation, and 
are (2) conjugate or functionally correspondent in relation to 
each other. 

Traditional theory, however, takes the propositions as given ready- 
made and hence as independent and complete in themselves. They 
are just there to be noticed, with description of whatever proper- 
ties they present. This mode of treatment becomes intelligible 
when it is viewed in conjunction with its derivation from the onto- 
logical logic of Aristotle, whence it ultimately derives. In the 
latter logic, species or kinds are the ultimate qualitative wholes or 
real individuals. Some of these species are by nature, or by in- 
herent essence, exclusive of others. The negative proposition was 

181 



182 THE STRUCTURE OF INQUIRY 



thus a cognitive actualization of a fundamental ontological form. 
Species also are ordered hierarchically. Hence affirmation of in- 
clusion of some species in species that are more comprehensive was 
also a cognitive actualization of the ontological. 

Positive and negative propositions are on this basis immediate 
apprehensions or "notations" of what exists in and by nature. 
What has just been said applies also to universal propositions — i. e., 
to those about wholes. Similar considerations apply to particular 
propositions, and hence to the so-called square of opposition with 
its relations of contrariety, sub contrariety, contradiction and sub- 
alternation. Things that change are by inherent nature incom- 
plete and partial. Hence they are apprehended in particular 
propositions. The connection between partial and particular was 
more than etymological. In traditional formal theory "some," 
the verbal mark of the particular, has come to mean "some, per- 
haps all." But in the Aristotelian theory, some meant some only. 
By the ontological nature of the case, wherever the affirmative 
"some are" applies, the negative proposition "some are not" holds 
also. The relation of subcontrariety was as ontological as was 
that of the contrariety of mutually exclusive universals. Particu- 
lars, or that which by nature is incomplete, because changing, 
can be known only through fixed limits imposed by the essence 
that defines a universal. Consequently, subalternation is in so 
far ontologically grounded. As for contradiction, it is evident 
that a proposition which is restricted by its ontological subject- 
matter to some only contradicts a proposition which by nature is 
about a whole. 

The development of modern science destroyed the conceptions 
of fixed species, defined by fixed essences, upon which the Aris- 
totelian logic rested. This destruction affected, therefore, the 
classic conceptions of universal and particular, whole and part, and 
the scheme of their relationships with one another. Modern logic, 
however, attempted to retain the scheme but with the understand- 
ing that it is purely formal, devoid of ontological import. The 
inevitable consequence is the mechanical way in which affirm- 
ative and negative propositions and their relationships are con- 
ceived in both traditional and modern formalistic logic. They 



AFFIRMATION AND NEGATION 183 

have lost their ontological basis without gaining a functional re- 
lation to the conduct of inquiry. 

The old designation, quality of propositions, is retained in con- 
nection with affirmative and negative propositions but is hardly- 
more than a mechanical label. From the standpoint of the func- 
tional connection of positing and negating with determination of 
unsettled or indeterminate situations, they are means, through the 
operations of selection and elimination they respectively prescribe, 
of ^qualifying the original indeterminate situation. Affirmative 
propositions represent the agreement of different subject-matters 
in their evidential capacity; they agree in that they support or 
are taken to support one another cumulatively in pointing in the 
same direction, in spite of the fact that existentially the subject- 
matters involved occur at different times and places. Negative 
propositions, on the other hand, represent subject-matters to be 
eliminated because of their irrelevancy or indifference to the 
evidential function of material in solution of a given problem. Ul- 
timately, the fact that certain facts or ideas are excluded means that 
the original indeterminate situation can be transformed or re- 
qualified into a determinate one only through existential experi- 
mental operative elimination of some of its constituents; affirma- 
tion of certain data or ideas means that they are operatively 
selected to reinforce one another in institution of a unified situa- 
tion. If these statements sound odd in contrast with the traditional 
interpretation of affirmation and denial, one has only to think of 
what happens in the conduct of scientific inquiry to see that they 
have a solid base and a pertinent meaning. 

That inquiry selects appropriate evidential data by means of 
comparison of what is found to exist or occur in different existen- 
tial cases is a commonplace. Without collection of phenomena 
observed at different times and places under different conditions, 
grounded inquiry, whether of common sense or science, can make 
no headway. Deliberate experimentation is resorted to for the 
express purpose of varying conditions, or so that observed conse- 
quences will so vary that comparison may have more extensive 
and more definite subject-matter to operate with. Collection of 
many cases with a view to institution of differences and agreements 
(in evidential force) is a kind of relatively uncontrolled experi- 



184 THE STRUCTURE OF INQUIRY ___ 

mentation. Comparison is so involved in all inquiries that reach 
grounded conclusions it is usually taken for granted. 1 

Now it is impossible to define comparison except operationally. 
It is a name for all operations in which identities and incompati- 
bilities in evidential force are determined. It is a name for any and 
all of the operations by means of which alleged or provisional data 
are determined to be data with respect to the problem set by a 
given indeterminate situation; by which some facts are determined 
to be the "facts of the case" in hand and other facts not to be. 
It is impossible to give an independent definition of comparison 
and then derive the operations of establishing agreements and 
differences in evidential capacity from that definition. It is a 
blanket term for the entire complex of operations by which some 
existences are selectively instituted as data and other existential 
materials are eliminated as having nothing to do with the case; as, in 
fact, obstructive in the required work of requalification of the 
existential situation. 

Mr. Bosanquet, one of the idealistic logicians referred to above, 
says "Comparison in the ordinary sense is a name applied to the 
intentional cross-reference of two or more given contents, in 
order to establish between these contents as given, a general or 
special identity, or partial identity (likeness)." 2 The view ex- 
pressed in this passage serves to bring out, by contrast, the meaning 
of the position here held. The italicized words of the text cited, 
as given, involve, positively, an affirmation of the antecedent on- 
tological basis of comparison and, negatively, a denial of the func- 
tional or operative force of propositions of identity — agreement — 
and difference — contrariety, subcontrariety, and contradictoriness. 
In contrast, the position of the text is that what is meant by com- 
parison is institution of selected facts on the basis of equivalent 
(similar) evidential force in a variety of cases which are existen- 
tially different, this determination being grounded only as the 
operations of observation involved in the selection eliminate, pari 

1 Examination of logical texts will show that the word rarely appears. The 
exception to this statement is found in the case of the writings of logicians of the 
rational idealistic school. They are interested in it as a somewhat elementary 
exemplification of their ontological proposition that "reality" as such is always 
a system of differences-in-identity or identity-in-diiferences, or what is called 
the "concrete universal." 

2 Logic, Vol. II, p. 21, italics in original text. 



AFFIRMATION AND NEGATION 185 

passu, other existential constituents as irrelevant to the problem in 
hand; as non-evidential, and indeed misleading unless eliminated. 
The view of Mr. Bosanquet reduces comparison to an act that can 
be and is performed within the "mind." The view here taken is 
that it is operational in the existential sense of effecting modifica- 
tions in what antecedently existed — as does controlled experimenta- 
tion. "Similarity" is the product of assimilating different things 
with respect to their functional value in inference and reasoning. 
There is much common sense inference in which similarity is im- 
plicitly postulated. When the assumption is stated in a proposition 
(as it needs to be if the conclusion of inquiry is to be grounded) a 
proposition of similarity is, in effect, an affirmation that there is 
sufficient probability of equal values to serve as ground for tenta- 
tive assimilation. 

The foregoing discussion has contrasted a theory of affirmation 
and negation based upon the practice of present scientific inquiry 
with the Aristotelian doctrine and with that later formalization of 
his doctrine which emptied it of all content. The connection of 
our view with the general theory of judgment will now be con- 
sidered. Indeterminate situations are marked by confusion, ob- 
scurity and conflict. They require clarification. An unsettled 
situation needs clarification because as it stands it gives no lead 
or cue to the way in which it may be resolved. We do not 
know, as we say, where to turn; we grope and fumble. We 
escape from this muddled condition only by turning to other 
situations and searching them for a cue. What is borrowed pro- 
vides a new attitude as the means for directing observational 
operations — performed on the common sense level through sensori- 
motor organs. These operations make some aspects of the given 
situation stand out. The attitude, when made explicit, is an idea 
or conceptual meaning. 

The very operations that select certain conditions, taken as 
potential clews to the problem to be dealt with, also rule out other 
conditions and qualities of the total given situation. Selection 
involves rejection and the latter act is rudimentary negation. The 
unsettled situation is also usually such as to evoke contrary modes 
of response. Attitudes and habitual modes of treating situations 
clash. This conflict is involved in confused and blind situations. 



186 THE STRUCTURE OF INQUIRY 

But sometimes the conflict is so uppermost that the main problem 
is that of reduction to unified significance rather than clarification. 
Some constituents stand out but point in opposed directions. To 
solve the problem resort must be had to other experienced situa- 
tions. These suggest additions and eliminations which, when ef- 
fected, will bring together the materials that first evoked conflicting 
responses. 

The process of eliminating materials that are irrelevant and 
obstructive goes hand in hand with that of rendering other ma- 
terials definite in their indicative force. Negation is thus the 
restrictive side of the selection involved in all determination of 
material as data. What is selected is provisionally positive. This 
positive phase is at first identical with taking and using the ma- 
terial in order to try it out. But control of this taking and using 
demands that the material be formulated. The propositions (that 
are the formulation) thus differ from the final assertion which is 
characteristic of judgment. Dependence of the rejection-selection 
operation upon suggestions supplied by other situations explains 
the emphasis put, in the traditional theory, upon "common" factors 
and upon agreement. Comparison is at the same time contrast, 
expressed in the rejection and the elimination of those elements 
and qualities in the situation which other situations indicate are 
irrelevant. 

It is sometimes said that affirmation and negation cannot be 
made coordinate with each other because there then arises a re- 
gressus ad infinitum. Such would be the result if they trod upon 
each other's heels. But in fact they are strictly conjugate. Not 
only is all determination negation but all negation is (or moves 
in the direction of) positive determination. The relation of 
affirmation-negation is no more successive than the taking of food 
by an animal is prior to or after rejection of other materials as non- 
food. Acts "which at one and the same time accept for use and 
that shut out are not sequential. 

The connection between organic selection-rejection and logical 
affirmation-negation is, moreover, a special case of a general prin- 
ciple already laid down. The organic function provides the 
existential basis of the logical. Transition from one to the other 
occurs when the direct existential commitment involved in organic 



AFFIRMATION AND NEGATION 187 

acceptance-rejection is deferred till the functional capacity of 
materials has been determined in inquiry. This postponed de- 
termination is made possible by language, by propositions about 
final decisive action. There are, for example, historical reasons for 
believing that processes of blame and accusation in connection with 
attempts to support and refute allegations were a main factor in 
developing the positive-negative aspect of inquiry. Then came 
argumentation pro and con in relation to some proposal advanced 
for social adoption. Argument still means reasoning. Crimen 
means judgment in the Latin tongue, and its root is found in our 
words discrimination and crime. The Greek aitia, usually trans- 
lated cause, had a definitely legal origin. Transition from the 
cultural to the logical status is manifest in the change from assent 
and dissent to affirmation and denial on specified grounds. To 
admit and to refuse to admit may be acts performed either for social 
reasons or because of reference to demands that are imposed by 
grounded inquiry. In the latter, they have explicit logical status. 
Affirmation is unambiguously a logical term. We affirm only that 
which we take to be capable of confirmation. 

There is another objection to the idea that affirmation is logically 
coordinate with denial. When the functional nature of affirma- 
tive propositions is overlooked — that is, their office in institution 
of data and meanings to be operatively employed— they are given 
direct existential reference. They are taken to be declarative of 
what is existentially there. The same thing cannot be said of 
negative propositions. Hence it is denied by some writers that 
negative propositions have any logical import at all. They are 
at most, according to them, rejections of suggestions that have 
arisen in our own minds and hence they have only a personal or 
psychological standing. In the words of one writer on logic 
"There is no such thing as a negative copula but only a negated 
copula." 3 

Mere negation, however, reminds one unpleasantly of the dis- 
putes of children, consisting of reiterations of "Tis, Tisn't." The 
important point is that the view in question follows from the 
postulate that all propositions about fact are complete and final 
because enunciative of antecedent existence. The doctrine which 

3 Sigwart, Logic, Vol. I, p. 122. 



188 THE STRUCTURE OF INQUIRY 



denies logical standing to denials thus gives indirect support to the 
position they are instrumental and functional. Existences and 
meanings are referred to, both in affirmation and negation, not 
just for the sake of mentioning them, but with respect to their 
function in requalification of an indeterminate situation; for this 
requalification can be effected (with respect to negation) only by 
elimination of obstructive materials and of suggestions that lead 
nowhere. If negative propositions are ruled out of the logical 
domain, comparison must go too. 

In short, negation is other than mere omission or dropping out 
of certain considerations, factual and ideational. Some facts and 
some meanings have to be actively eliminated because they are 
obstacles that stand in the way of resolution of an unsettled situa- 
tion. The idea that negation is connected with change, with be- 
coming other or different, is at least as old as Plato. But in Plato 
change, altering or othering, has a direct ontological status. It 
is a sign of the defective ontological character of that which 
changes, its lack of full Being. The negative proposition, which 
dealt with change, was thus the counterpart in knowledge of the 
ontological inferiority of one kind of existential material. But in 
modern science, correlations or correspondences of change are the 
chief object of determination. It is no longer impossible to treat the 
relation of the negative proposition to change and alteration as 
declarative of defective being. On the contrary, the negative 
proposition as such formulates a change to be effected in existing 
conditions by operations which the negative proposition sets forth. 
It is an indication of an experimental operation to be performed 
such that conditions will be so varied that the consequences of the 
operation will have an evidential significance lacking in the condi- 
tions as they existed at first. 

The affirmative proposition also has intrinsic connection with 
change. Take the proposition "This is red." On its face, it is 
purely affirmative; it carries with it no suggestion of negation or 
elimination. But the bare existence of a red thing is not a suffi- 
cient ground for the affirmation that "It is red." To be grounded, 
alternative possibilities must be ruled out. There is no logical 
necessity why this should be red; it may have been some other 
color a moment ago and become another color a moment from 



AFFIRMATION AND NEGATION 189 

now. The proposition is "synthetic" in the Kantian sense; it can- 
not be grounded in a mere intellectual analysis of this. Valid 
determination that "this is red" depends upon (1) exhaustive dis- 
junction of alternative possibilities of color and (2) upon elimina- 
tion of all other possibilities than the one affirmed, the elimination 
resulting (3) from a series of hypothetical propositions such as 
"If blue, then such and such consequences," etc., in contrast with 
the proposition "If red, then such and such other and differential 
consequences." I do not mean of course that as a matter of fact 
such an elaborate process of determination is often gone through. 
I do mean, however, that for complete logical validity there is 
required a proposition like the following: "Only if this is red, 
will observed phenomena be what they are." "Ofily" in this prop- 
osition depends upon a series of eliminations expressed in negative 
propositions. Whenever a scientific determination of color quality 
is required in solution of a scientific problem, inquiry proceeds in 
the direction of just such an exhaustive disjunctive system and of 
systematic elimination of all alternatives save one for which positive 
grounds are found. 

The connection of this determination with deliberate institution 
of change should be obvious. A series of experimental operations 
has to be performed with and upon the existential material indi- 
cated by the demonstrative this. The changes which follow as 
consequences of the execution of these experimental operations 
provide grounds for denying that it is blue, yellow, purple, green, 
etc., and for affirming that it is red. If one is inclined to doubt 
this account, especially on the ground that the proposition in ques- 
tion, if not "self-evident," is at least not nearly as highly mediated 
as the account assumes, let him recall that scientifically color is 
determined only by operations which identify colors with certain 
rates of vibration, and red with one particular exclusive number. 
In other words, the proposition "This is red" means, logically, 
that a certain differential change has occurred or may be predicted 
to occur when certain operations are undertaken. In the latter 
case, the logical meaning is "This will become red or will redden 
something else," certain conditions being postulated. If the propo- 
sition be interpreted to mean "This has been red for a long time," 
even more extensive mediation is required to warrant a con- 



190 THE STRUCTURE OF INQUIRY 

elusion about the added trait of temporal duration. If it is taken 
to mean "It is red by nature or necessity," reference to change 
is excluded but this is the only case in which the proposition is 
not about a change. 

Impersonal propositions such as "It is raining" have been the 
theme of more or less discussion. The natural interpretation of 
such propositions is that in them a total prior qualitative situation 
is negated-affirmed by specification of a change. "It" refers to 
the gross environing perceptual field; "rain" to the gross alteration 
it is undergoing. If the proposition is "It is only sprinkling" or 
"It is raining hard," the qualification is more differentiated because 
more specific negations have been introduced. Propositions of 
gross qualitative change are the starting points for a set of dis- 
junctive propositions in which a single continuous change is 
formulated in terms of a scale or spectrum of degrees. It is not 
sufficient to take a gross change in its given discreteness. It has 
to be resolved into a series of changes, each of which is determined 
by reference to its position in a continuum of changes. Such 
determination involves a disjunctive set of propositions. In each 
determination of position in the scale a negation of all disjunctive 
possibilities except one is involved. 4 

After these general remarks, I come to the specific forms of the 
relations of affirmative and negative propositions designated as 
contrariety, subcontrariety and contradiction. From what has 
been said, it follows (1) that these relations have to be understood 
in the functional office they exercise in inquiry, (2) as correlative 
or conjugate determinations, not as independent sets of propo- 
sitions which happen to sustain to each other the relation des- 
ignated. (The ordinary square of opposition is likely to be 
interpreted in the latter sense, since failure to connect the proposi- 
tions which are contrary, etc., with the process of inquiry has the 
effect of setting-up a purely mechanical scheme of propositions 
each logically independent of the other.) 

I. Contrariety or logical opposition obtains between affirmative 
and negative propositions when both are general. The relation is 
such that only one can be valid and both may be invalid. The 
relation between "All marine vertebrates are cold-blooded" and 

4 The topic of scales receives further attention in the next chapter. 



AFFIRMATION AND NEGATION 191 

"No marine vertebrates are cold-blooded" exemplifies the relation 
of contrariety. Contrariety of propositions sets the limits within 
which specific determinations must fall In themselves, they are 
indeterminate; that is, if they are taken as final and complete, 
rather than as expressing a certain necessary stage in the progress 
of controlled inquiry, they are logically defective. This logical 
defect is apparent in the fact that both may be invalid. Contraries 
are a stage in institution of the set of exhaustive disjunctives which, 
as we have seen, are required for adequate affirmative-negative 
determinations. They do not of themselves constitute the re- 
quired disjunctives, for (as is evident in the illustration just given) 
they permit of alternatives, such as "Some are and some are not." 
But they set the limiting termini for intermediate alternatives. 
They serve to delimit the field of inquiry, and thereby to give 
direction to subsequent observational and ideational operations. 
The traditional A and E propositions represent the limits within 
which alternatives fall, but the fact that both may be invalid 
proves that they do not do more than that. As contraries, they 
represent, then, not conclusions but the results of a preliminary 
survey of the total problematic field, the survey being made to 
circumscribe the field within which further determinations must 
occur. A process of groping reaches its initial termination when 
we can state the extreme boundaries within which a solution must 
be sought. 

We have, then, the following logical situation. (1) On the one 
hand, the field of possible propositions must be bounded or else 
inquiry will roam all over the lot. This delimitation is effected 
by means of contrary general propositions. (2) On the other 
hand, when the strictly functional nature of the propositions 
having the relation of contrariety to each other is overlooked, 
these delimiting propositions are supposed to exhaust possible 
alternatives. Then the rigid type of Either-Or reasoning results, 
a type which is common in thought about social and moral 
issues. Either "The Individual" or "Society" as a fixed entity; 
either freedom from all restraint or coercion from without; either 
the bourgoisie or the proletariat; either change or the unchanging; 
either the continuous or the discrete, and so on. Only when the 
strictly functional nature of contrary propositions is seen do we 



192 THE STRUCTURE OF INQUIRY 

escape from the unending and inherently endless round of con- 
troversies generated by this mode of thought. When their func- 
tional and instrumental nature is perceived, they are seen to be 
necessary, but necessary only because they set the boundaries 
within which a set of more determinate disjunctive alternatives 
are to be sought for. They are functional directives for further, 
more discriminating, determinations. 5 

In logical theory, the rigidity and hence apparent finality of 
contrary propositions is often enforced by use of symbols that 
have no meaning or content of their own. A and Not~A are, for 
example, such symbols. These purely formalistic contraries can- 
not possibly have directive force. For if, say, "virtue" be assigned 
to A as its meaning, then Not-A includes not only vice but trian- 
gles, horse races, symphonies and the precession of the equinoxes. 
Since the time of Aristotle, the nugatory nature of "infinitation of 
the negative" has been generally recognized. "What has not been 
so generally recognized is ( 1 ) that failure to recognize the inter- 
mediary function of contrary proposition tends in the direction 
of infinitation, and (2) that any purely formalistic either-or formu- 
lation of contraries (such as A and Not-A) eliminates reference 
to any universe of discourse and, hence, when any value is assigned 
to the positive expression, renders the negative wholly inde- 
terminate. Nevertheless, the institution of opposites in hypo- 
thetical form, when interpreted as a means of fixing the limits 
within which determinate disjunctive alternatives fall, is a necessary 
preparatory logical procedure. 

II. Subcontrary propositions of the form "Some are . . ." and 
"Some are not" may both be valid while one must be valid, when 
they are determinate. "Some marine vertebrates are cold-blooded" 
and "Some are not" are subcontraries both of which are now 
known to be valid. The phrase "are now known" is related to 

5 The dialectic of thesis, antithesis and synthesis recognizes that the initial con- 
traries are not final. But it suffers from the logical vice of supposing that the 
"synthesis" grows directly out of the contraries, instead of from determinate in- 
quiries which the contraries indicate. In scientific inquiry, thesis and antithesis are 
never treated as generating a synthesis. For example, the relationship between 
"heredity" and "environment" as contraries sets an important problem, as at one 
time in physics a problem was set by the relation of centrifugal and centripetal 
"forces." But the scientific problem is handled by means of analysis of the 
subject-matter of these highly general terms into specific conditions, not by 
manipulation of the concepts. 



AFFIRMATION AND NEGATION 193 

the clause in the previous sentence "when they are determinate." 
The formal logical relation involved is, in other words, a form of 
existential contents determined by observation. However, like 
any form, it may be abstracted, while the abstract form has logical 
meaning only in its possible application to material contents. As 
far as mere form is concerned, both of the propositions cited might 
be invalid. For apart from what is existentially determined, the 
valid proposition might be "No marine vertebrates have blood." 
Only because a conjunction of the traits of possessing a spinal 
column and possessing blood has already been established, are the 
propositions subcontraries. 

Subcontraries are more determinate than contraries but are still 
indeterminate as compared with final judgment. For fully de- 
terminate propositions regarding the subject-matter in question 
would be u All marine vertebrates marked by -such-and-such traits 
(say, bringing forth young alive and breathing with lungs) are 
warm-blooded" and u All marine vertebrates having such-and-such 
other differential traits are cold-blooded." If they were final and 
complete, subcontrary propositions as logical forms would be even 
more slovenly than contraries. As a matter of fact, however, 
they record the results of observation in such a way as to provide 
factual data that set a definite problem. The subcontrary proposi- 
tions cited represented the state of zoology at a given date when 
the discovery of two kinds of marine vertebrates, marked off by 
differences in quality of blood, definitely set a problem; namely, 
the problem of discovering the conditions in which some marine 
animals are of one kind and others of another kind. It did so 
because of a material postulate, namely the postulate that blood 
plays such an important role in animal life that a difference with 
respect to it is, to a high degree of probability, bound up with 
other important characteristics. Propositions marked by "some," 
affirmative and negative, thus present the results of a relatively in- 
complete empirical state of inquiry, where "empirical" means a 
valid statement of results of actual observation without insight 
into the conditions upon which observed traits depend. The de- 
pendence of valid conclusions in existential matters upon factual 
observation shows that such propositions, while not final, represent 



194 THE STRUCTURE OF INQUIRY 



a definite stage in the conduct of inquiry and perform a necessary 
office in carrying it forward to a conclusion. 

Inquiry with respect to light is at the present time in this 
stage. There are grounds for holding that "Light in some respects 
is a radiant phenomenon and in some respects is not, being cor- 
puscular." Granting the adequacy of the observations upon 
which these propositions rest, no one will deny that they mark 
a scientific advance. On the other hand, few would contend that 
scientific inquiry can be content with these propositions as final. 
They institute a definite problem for further investigation: Under 
what conditions is light vibratory and under what conditions is it 
discrete? 

III. The discussion of subcontrariety leads up to the conception 
of subalternation. If it has once been determined that all marine 
vertebrates marked by a specified conjunction of traits are warm- 
blooded, the so-called subaltern that some such animals are warm- 
blooded is trivial. Reference to the general proposition may serve 
upon occasion as a reminder to some person who is temporarily 
forgetful, but it has no logical force. Suppose that inquiry at a 
certain stage has determined only that in the case of a shipwreck 
some passengers have been saved and some lost. Suppose further 
inquiry determines specifically the names of all who are saved and 
all who are lost. In the latter case, it is silly to recur to the 
weakened form "some" when the tabulated list of all of each kind 
is at hand. The name of any given person must appear in one 
list or the other. About a specified person there are no alternatives. 

The real function of the proposition of the form of some is in 
the opposite direction from that of the traditional table. Instead 
of movement from "all" to "some," there is a reaction from some 
into all. At an early stage of inquiry that "some" are saved indi- 
cates that perhaps "all" on board have been saved. At the stage 
when the inquiry is completed, the transition is from the indefinite 
"some" of "all" who were on board, to all of a specified group. 
In a strictly empirical proposition (in the sense of "empirical" 
defined above), there is no difference in logical form between the 
proposition "All cases so far observed are such and such" and the 
proposition "Some cases out of all existential cases, past, present 
and future, are such and such." The logical sense of both lin- 



AFFIRMATION AND NEGATION 195 

guistic forms is "Perhaps all cases are such and such." When the 
conditions under which phenomena are such and such have been 
exclusively determined (through a set of affirmative-negative prop- 
ositions) then a general proposition in the form of a law is possible: 
Whenever conditions are such and such, consequences are such 
and such. 6 

IV. The foregoing analysis has one main purpose, namely to 
indicate, on one side, that when affirmative and negative proposi- 
tions are taken to be final and complete (as they must be when 
their operative connection with the progressive conduct of inquiry 
is ignored) the forms in question are mechanical and arbitrary; 
and, on the other side, to indicate that when their functional ca- 
pacity is taken into account the relations of contrariety, sub- 
contrariety and subalternation mark definite stages in the advance 
of inquiry toward a final warranted judgment. These considera- 
tions come, as it were, to a head in the case of contradictory propo- 
sitions, those that are such that if one is valid, the other is 
invalid, and if one is invalid the other is valid. In the traditional 
square of opposition this relation of contradiction is symbolized by 
the diagonal lines from the general affirmative to the negative 
particular (some, meaning one or more) and from the general 
negative to the affirmative particular. Formally speaking, it is 
certainly true that the proposition "all men are white" is contra- 
dicted if a single case of a colored person is observed, while the 
proposition "No men are red" was negated as soon as the first 
North American Indian was encountered. 

But the essential logical point here is that the general (affirmative 
or negative) is negated not by the indeterminate "some" but by the 
determinate singular. "Some" is logically either excessive or de- 
ficient. It is excessive, if a singular case has been determined (not 
in fact an easy matter) ; it is defective, if "some" is understood in 
its strict logical force, namely, as an indication of a possibility, of 
the form "may be" or "perhaps." The fact that a given Z or O 
proposition may be invalid is enough of itself to prove that it can- 
not contradict in any strict logical sense a general proposition of 
the opposite quality. The proposition "Some men are not white" 

6 The difference between the two kinds of general propositions in both of 
which the word all may appear is discussed in Chap. XIII. 



196 THE STRUCTURE OF INQUIRY 



indicates that an object may be colored and yet be a human being, 
or may be a human being and yet not be white. We are familiar 
with the warning against vague generalities. The warning is de- 
cidedly relevant at this point. "Some," if unspecified with refer- 
ence to singulars, is of the nature of a vague generality. If it is 
specified, then it assumes one of two forms: "Such and such 
determinate singulars are of a given kind," which negates a general 
proposition that "all are of some other kind"; or, still more deter- 
minately, "All singulars marked by specified traits are of a certain 
kind." In either case, it is not an indeterminate "some" which 
contradicts the general A or E proposition. 

As has already been indicated, the proposition about a number 
of (or some) singulars being such and such sets a problem. It 
suffices to negate a general proposition of the opposite quality. 
But the negation is in so far incomplete or indeterminate. It does 
not of itself establish a valid, universal proposition. It warrants 
a contradictory universal only when two logical conditions are 
satisfied: (1) Determination of a set of alternative disjunctives 
as exhaustively as possible, and (2) determination of the differen- 
tial traits which are evidential signs of one and not another kind. 
At a given stage of scientific inquiry, an exception is discovered 
to some previously accepted generalization. If careful inquiry 
substantiates the authenticity of the exceptional singular, then the 
generalization in its previous form is certainly negated. But no 
scientific inquirer would suppose for a moment that this negation 
was equivalent to establishment of a valid universal proposition. 
The question at once arises as to the exact conditions under which 
the exceptional and negative case occurs. As soon as this is done, 
we have another generalization: "All cases marked by certain 
traits are such and such." In short, the discovery of singulars or 
a singular that negates a generalization is but the antecedently 
conditioning means to further inquiries. The proposition in 
which it is embodied is not final or complete, for it functions as 
occasion and stimulus of further inquiries with view to determin- 
ing honv and ivhy the exception occurs. When these inquiries are 
satisfactorily concluded, then and only then do we have a final 
proposition, which takes the form of a new general proposition. 

In no case of controlled inquiry is a flat negation of a generaliza- 



AFFIRMATION AND NEGATION 197 

tion taken to be final If it were so taken, a former generalization 
would simply be abandoned and that would be the end of the 
matter. What actually happens is that the prior generalization 
is modified and revised by discovery of the contradictory instance. 
Certain data discovered by using the Einsteinian theory of rela- 
tivity contradicted the Newtonian formula of gravitation. If such 
negations had the independent and final logical status attributed to 
them by traditional formalistic logic, either the Newtonian for- 
mula would have been declared invalid and the matter would have 
ended there, or else the observational data would have been de- 
clared false and impossible because they contradicted the general 
proposition. Even in the cases in which an exception turns out 
to be apparent rather than actual, the older generalization is not 
simply confirmed, but gains a new shade of meaning because of 
its capacity to apply to the unusual and seemingly negative in- 
stance. It is in this sense that "the exception proves the rule." 

The logic of the contradictory relation of propositions thus af- 
fords a crowning proof of the functional and operative import of 
affirmative-negative propositions. Nothing is more important in 
inquiry than institution of contradictory propositions. Since one 
must be valid and the other invalid, they are determinate in a way 
in which contraries and subcontraries are not. But if the tradi- 
tional theory were sound, inquiry would have to stop right there. 
There would be no ground upon which to decide which one of 
the two is valid and which is invalid. Those who prefer to trust 
to the "evidence of the senses" would hold that the generalization 
had been proved false. Those who distrust sense and exalt "rea- 
son" would be inclined to reverse the conclusion and hold the 
singulars are not "really" what they seem to be. Institution of 
contradictories in the actual procedure of scientific inquiry is 
crucially important just because it does not adopt the canons of 
any theory that makes contradictories final and complete. In the 
conduct of inquiry, institution of a contradictory negation is 
treated as a step in the continuation of inquiry towards final 
judgment. The final effect is to revise the generalization reached 
in earlier inquiries. Through this modification a generalization 
becomes applicable to both the old evidential material which sup- 



198 THE STRUCTURE OF INQUIRY 

ported it and to the new evidential material which contradicts 
the earlier generalizations. 

The original Aristotelian conception of affirmation and nega- 
tion at least corresponded to what was supposed to be the onto- 
logical nature of the objects to which affirmative and negative 
propositions apply. The functional conception here advanced 
denies that affirmative and negative propositions have a one-to-one 
correspondence with objects as they are. But it gives them the 
operative and instrumental force of means of transforming an 
unsettled and doubtful existential situation into a resolved de- 
terminate one. The modern theory, derived, as has been said, 
from the attempt to retain forms after their material or existential 
content had been abandoned, is grounded in nothing and leads 
nowhere. It is formal only in the sense of being empty and 
mechanical. In neither reflects existence already known nor for- 
wards inquiry into what may and should be known. It is a logical 
vermiform appendix. 

In view of the fact that the metaphysical problem of the One 
and the Many has at various times had a very considerable influ- 
ence upon logical theory, it may be appropriate, in concluding 
this chapter, to say a few words on that topic as it affects logical 
theory. Unity, or what is termed The One, is the existential 
counterpart of the product of operations which, by institution of 
agreement of different contents in evidential force, establish war- 
ranted identities. Negation, on the other hand, discriminates and 
produces differences. The latter when hypostatized constitute the 
Many. The problem when approached from the logical side is 
one of operations of unifying and discriminating. These oper- 
ations have of course an existential basis and matrix. Integration 
and differentiation are biological processes foreshadowing the logi- 
cal operations just mentioned. They are themselves prepared for 
and foreshadowed in physical processes of conjunction and sepa- 
ration. The insoluble problems which have led to speculative 
metaphysical constructions about the One and the Many arise 
from making entities, expressed in nouns, out of processes and 
operations properly designated by active verbs and adverbs. 



CHAPTER XI 

THE FUNCTION OF PROPOSITIONS OF 
QUANTITY IN JUDGMENT 



"n traditional formal logic, the topic of quantity of proposi- 
tions follows after that of quality. The traditional theory, 

. applying to propositions with respect to both quality and 
quantity, holds that propositions are capable of interpretation on 
the basis of both extension and intension. In the former case, a 
proposition is of a relation of classes; in the latter, it states that 
members of a specified class are affirmed to be marked by a speci- 
fied attribute. As applied to quantity, in extensive interpretation 
a proposition declares either that a class as such is contained in 
another class and then is general in quantity; or that some unspeci- 
fied portion of it is so contained, and is particular in "quantity." 
When read in intension, a proposition states either that any mem- 
ber of the class has a certain "attribute" or that some unspecified 
portion of it has a given attribute. Thus, the "general" proposi- 
tion "All men are mortal" means either that the class men is con- 
tained as a sub-class in the class mortals, or that any man whatever 
has the attribute mortality. In any case, quantity, so-called, is 
according to this doctrine marked by the two forms all (none, not 
any) and some (some-not), a distinction which, in combination 
with that of the affirmative-negative yields the four forms of 
A E I O propositions. The slightest inspection thus reveals that 
the distinction or form called quantity is, in fact, that of the 
definite class and an indefinite part of a class. 

The extremely restricted conception of quantity involved in 
this theory hardly needs to be pointed out — restricted, that is, in 
comparison with propositions of common sense and of science 
which have quantitative marks. In common sense, there are 

199 



202 THE STRUCTURE OF INQUIRY 

Given the latter, propositions are marked both by quality and 
quantity. For purposes of discussion we must deal with one 
aspect or the other separately, but the separation is made purely 
for the sake of discussion. It has no counterpart in the subject- 
matter which is the ground and result of comparison. The 
connection of the function of elimination with the work of 
comparison need not be gone over again. What is here significant 
is that all comparison is of the nature of measurement. Compari- 
son obviously involves selection-rejection, for objects and events 
cannot be compared in toto. The positive import of this fact is 
that in order to be compared, subject-matters must be reduced to 
"parts"; that is, to constituents that are capable of being treated 
as of the same kind or homogeneous. To compare is to pair, and 
things that are paired are thereby made commensurate with respect 
to carrying out some operation in view. 

The only difficulty standing in the way of recognition of the 
equipollence of comparison and measurement is the fact that the 
results of many measurements are stated qualitatively, not in nu- 
merical terms. There is at the very outset a fundamental ambi- 
guity in the conception whole-part. In one sense, it is entirely 
qualitative. To be a whole is to be complete, finished; to be of 
seamless quality throughout. If parts are mentioned in connection 
with such a whole, nothing separable and removable is denoted. 
The most familiar instance of such "parts" are the organic mem- 
bers of a living body. If they are removed, they are no longer 
what they were as living "parts" of the living organism, while the 
latter is no longer a complete whole. It is not necessary, however, 
to go to so-called organic relations to find instances of qualitative 
whole-parts. In what is termed a situation, an immediate quality 
pervades everything that enters into that situation. If the situation 
experienced is that of being lost in a forest, the quality of being 
lost permeates and affects every detail that is observed and thought 
of. The "parts" are such only qualitatively. 

The term "all" is still frequently employed in connection with 
qualitatively unified wholes: "It is not all of life to live," "All flesh 
is as grass which today is and tomorrow is cast into the fire," "It 
is all gone," "The fire is all out," "All the invited guests have now 
arrived" in the sense that the gathering is now complete — not in 



QUANTITY AND MEASUREMENT 203 

the sense of an enumeration. The quantitative meaning of whole- 
part is, on the other hand, either that of a collection or of an aggre- 
gation of homogeneous units such that the whole in question has its 
magnitude or amount determined by counting comprised units. 
There are cases of comparison-measurement which lie between 
the two limits set by the strictly qualitative and quantitative 
wholes. Common sense propositions marked by more-less, by the 
so-called comparative degree, as hotter-colder, taller-shorter, many- 
few, much-little, etc., are of this category. They represent meas- 
urements, but not measurements carried to the point of numerical 
determination. It is these intermediate cases which tend to ob- 
scure the connection of comparison with measurement. 

From these introductory remarks, discussion proceeds to con- 
sideration of propositions marked by quantitative terms (1) to 
indicate more explicitly their connection with comparison, (2) to 
indicate their operational and intermediate force in determination 
of final judgment, and (3) to indicate the various logical forms 
they assume. The first topic is introduced by noting that the 
situation which evokes inquiry and which induces the formation 
of propositions as means to its final determination is indeterminate 
for the reason that, as it stands, it is both too wide and too narrow 
to provide the data that signify and that test proposed methods of 
resolution. The indeterminate situation is both deficient and 
redundant. Elimination of what is superfluous and obstructive 
and provision of what is lacking with respect to evidential ca- 
pacity, are indispensable. The satisfaction of these requirements 
through the function of affirmation-negation has been dealt with. 
But redundancy and deficiency are also quantitative concepts in 
a quasi-qualitative form. What is termed in logic the undistrib- 
uted middle is an instance of a too great width of subject-matter 
which incapacitates it to serve as ground; so also is the fallacy of 
affirming the antecedent because the consequent is affirmed. 

The rule that from two particular propositions nothing can be 
inferred is on the other hand a warning that material in hand is 
too narrow to warrant a grounded inference. It is in effect a 
statement of the need for supplementation. In examples used in 
standard texts, the fallacies which result from too wide and too 
narrow subject-matter are readily detected, because they concern 



204 THE STRUCTURE OF INQUIRY 

material already cooked or loaded. In actual inquiry a large part 
of the task is to determine just what subject-matter needs to be 
eliminated and provided and how. It required, for example, two 
centuries before the too great width of Newtonian conceptions of 
space and time was detected, and it took inquiry much more time 
than that to discover the narrowness of the ancient conception of 
atoms and corpuscles that unfitted it for scientific use. The 
only method for modifying subject-matter which is indeterminate 
because of overlappings and because of insufficiency is the weight- 
ing secured through measurement. 

Measurement, as has been said, assumes at first a qualitative 
form. Propositions marked by such words as much, little, few, 
many, a whole lot, scanty, abundant, small, great, high, low, etc., 
etc., express measurement as far as they go. For there is nothing 
which is much, little, etc., absolutely or by itself. Moreover, 
these determinations not only involve comparison but they also 
involve the means-consequence relation. There is too much or 
too little for a specified end, not per se; "I should like to buy that 
article but I haven't enough money"; "Some people in this country 
have too much money for their own good and for that of the 
country." The beginning of the formation of a balance sheet in 
such cases takes the form of subcontrary propositions. "Some 
money is at hand and some is not." "Everybody needs some 
money, but no one needs more than a certain (not definitely speci- 
fied) amount." Such propositions have rudimentary quantifica- 
tions, but the quantities involved are still predominantly qualitative. 
Measurement or comparison becomes definite by means of count- 
ing and summing units. Then we have a whole-of-parts in specifi- 
cally quantitative meanings of this term. Much becomes how 
much; many, how many. 

It is not, however, to be inferred that in all cases qualitative 
measurement is so defective that, in order to be adequately de- 
terminate, it needs to pass into numerical measurement. For ex- 
ample, a painter at work upon a picture may decide that there 
is not enough red in a certain part of the picture to give the desired 
esthetic effect. He determines how much red should be added 
by "intuition" and trial, stopping when he gets the qualitatively 
unified whole he is after. He appraises or evaluates the amount 



QUANTITY AND MEASUREMENT 205 

needed on the basis of a net qualitative outcome, not by weighing 
a pigment upon a scale having numerical indices. Were the case 
one of regulated economical industrial production, the weighing 
of amounts would certainly take the form of numerical determina- 
tion. In most moral as well as esthetic final judgments, qualitative 
measurement answers the end to be reached. Insistence upon nu- 
merical measurement, when it is not inherently required by the 
consequence to be effected, is a mark of respect for the ritual of 
scientific practice at the expense of its substance. 

In the case of both qualitative and numerical measurement, some- 
thing has to be taken away and something added. In this sense, 
measurement in qualitative terms, more, less, enough, etc., ap- 
proximates the quantitative part-whole relation. The difference 
between the two cases concerns the method and criterion of 
measurement, not its presence or absence. The nature of the end 
to which measuring is relative determines both criterion and the 
method employed. It is as absurd to insist upon numerical meas- 
urement when the end to which the quantitative proposition is 
related as means to consequence is qualitative, as it is to be content 
with qualitative measurement (which is then guess-work) in the 
case of other ends-in-view. 

In the case of the painter, the intended end is the picture as a 
qualitative whole. More of this color and less of that is therefore 
capable of measurement by direct qualitative observation. More 
red here affects not just the spatial part of the picture in which it 
is applied but the picture as a whole; other hues and shades are 
made qualitatively different by its application. In the case of a 
medical prescription, on the other hand, too much of an ingredient 
may change a medicine into a poison and too little may render it 
medically innocuous. Numerical measurement is then demanded 
by the end to be attained. It is ultimately the nature of the prob- 
lem in hand which decides what sort of comparison-measurement 
is required in order to obtain a determinate solution. There are 
some persons who deplore the reduction by the scientist of all 
materials to numerical terms on the ground that it seems to them 
to destroy value which is qualitative. There are other persons 
who insist that every subject-matter must be reduced to numerical 
terms. Both are guilty of the same logical error. Both miss the 



206 THE STRUCTURE OF INQUIRY 

logical meaning of measurement, which is determined by the in- 
strumental reference of quantified propositions to an intended ob- 
jective consequence. Both take propositions as ultimate and 
complete, when, in fact, they are intermediate and instrumental. 

That one important difference between common sense and 
science is constituted by the tendency of the former to be satisfied 
with measurement that is dominantly qualitative is obvious. For 
practical ends it is enough to speak of a big crowd, or of the room 
growing warmer or colder, the day becoming brighter or duller, 
etc., whereas to satisfy the demands of technology, business, and 
science numerical comparisons are required. The box-office, for 
example, wants to know just how large or how small is the "crowd" 
in the theater; the careful householder wants a thermostat to keep 
variations of temperature within definite limits; the worker in the 
laboratory has to measure numerically just how much of each 
material and of each form of energy is involved in production of 
the phenomenon he is studying. All cases, however, whether of 
common sense, technology, business or science, explicitly reveal, 
when they are examined, the means-consequence relation, thereby 
disclosing the intermediate nature of propositions of quantity as 
instrumental in determinate resolution of an otherwise indeter- 
minate situation. 

It is often said that the conception of quantity rests upon com- 
plete indifference to quality. On this ground it is claimed, par- 
ticularly by logicians of the idealistic school, that the concept of 
quantity so abstracts from the "real" world as to represent a low 
grade of "thought." This view is based upon failure to realize 
the operational character of propositions about quantity, whether 
extensive or intensive. But the notion of indifference to quality 
is also exposed to radical misconception. For the correct state- 
ment is that propositions about magnitude are based upon an 
underlying pervasive quality, and are indifferent only to differ- 
ences within this basic quality; that is, they are indifferent to those 
qualities and only those qualities within the basic quality which are 
irrelevant as means to the consequences to be established. If, for 
example, a person is trying to frame a proposition about the num- 
ber of sheep he owns or the area of the pasture in which they 
feed, he neglects qualitative differences that mark off individual 



QUANTITY AND MEASUREMENT 207 

sheep from one another and qualitative differences in different 
portions of the field in which they feed. But he has to observe the 
quality in virtue of which objects are sheep, or else he will count, 
say, dogs and stones. He has similarly to observe the quality in 
virtue of which grass-land is of the kind it is. The logical import 
of this commonplace remark is that it indicates in general (1) the 
control of propositions of magnitude by the quality of the situation 
to which the problem of inquiry is relevant, and in especial, (2) the 
importance and logical nature of limits. 

The first point has already been sufficiently emphasized. 1 The 
import of the second point is at least suggested by the negative 
fact that the presence of limits in all counting and measurement 
that have existential reference (and it is only propositions having 
such reference that are under discussion) affords a complete an- 
swer to the objection brought by idealistic logicians against the 
validity of such propositions: viz., that they necessarily involve a 
regressus ad infinitum. Stated positively, all such measurement 
(including the case of enumeration) has its limits set, on one side, 
by the problematic subject-matter in hand and, on the other side, 
by the definite resolution which inquiry undertakes to effect. 
These considerations determine the meaning of the determinate 
all and of the indefinite some. They also fix the difference be- 
tween two kinds of collective propositions in each of which the 
word all appears: "All the books on that shelf are novels"; "All 
the guests have arrived"; "The tide is all in or all out" — that is, is 
high or low; "The iron is tf/ready soft enough to work"; "The 
bowl is full of as much water as it will hold." In the last three 
cases qualitative wholeness predominates, though the propositions 
are certainly dependent upon comparison and involve measure- 
ment. In the first two cases, there has to be observation of each 
singular in order to warrant the propositions made though not in 
the later propositions. 

Nevertheless, there is an aspect of totality involved and hence of 
inherent objective limitation in each instance. The propositions 
are not collective in the sense of mere aggregates of enumerated 

x It is sufficient, however, to negate the idea that a scientific proposition is 
merely a numerical-index, to the exclusion of any symbol having reference to the 
qualitative. 



208 THE STRUCTURE OF INQUIRY 

units. The shelf is full of books of a kind; the quota of guests is 
complete. All in some other propositions has still a third meaning, 
and this meaning, in spite of the word all, relegates the propositions 
in question to the category of the particular form. "AH of the 
beans in this bag which have so far been examined are white." "No 
person who has as yet entered the hall is an acquaintance of mine." 
"Altogether the stamps in this collection number 874." In such 
instances, the enumeration of singulars does not determine a limit 
nor yet even indicate that a limit has been reached; there is no 
intimation that anything having entirety is exhaustively deter- 
mined. For logical purposes, the first proposition is equivalent to 
the proposition "some beans in this bag are w T hite, and perhaps all 
are," the probability depending upon the number examined in its 
ratio to the total number in the bag — the latter setting a qualitative 
limit. Confusion arises when application of the word collective 
to such propositions is used to assimilate them, in logical theory, to 
collections in which a limit is reached or set. That a regiment 
consists of so many companies and each company of so many 
men is a collective proposition in a very different sense from a 
proposition about the number of books in a library or the number 
of stamps in a "collection," just as the proposition that "this room 
contains so many cubic feet" is different in form from the propo- 
sition "this sand pile contains so many grains of sand." The dif- 
ference will hereafter be noted by calling only the former col- 
lective, while the latter will be called aggregative. 

The distinction that has been drawn bears directly upon the 
status of propositions in which some is explicitly present. We may 
recur to the illustration in the last chapter regarding persons on a 
shipwrecked vessel, placing the emphasis now not upon affirma- 
tion, but upon some "are saved" and some "are lost." The affirma- 
tion "Some are saved" and the negative proposition "Some are not 
saved" are clearly indeterminate; the indeterminacy is manifest if 
we suppose that a person having a friend on board is solicitous 
about his friend's fate. Until singulars are determined and then 
gathered together in a proposition that reaches an objective limit, 
the propositions cited refer to indeterminate aggregates. When the 
needed operations are performed we have a collection that is other 
than aggregative. "All the following persons (definitely specified) 



QUANTITY AND MEASUREMENT 209 

were saved and all the following named persons were lost." There 
is now a double qualitative limitation. There is the qualitative limit 
of completion set by the total number of persons on board and by 
the quality of being lost or saved. 

So far it has been shown in what sense "all" is the mark of a 
quantitative proposition, differentiating such a proposition, (1) 
from mere aggregates (which in their indefiniteness do not differ 
logically from propositions in which "some" appears); and (2) 
from the "all" of non-existential propositions (such as "all triangles 
have the sum of their angles equal to right angles") which, when 
valid, are necessary propositions; and (3) from "all" in such 
propositions as "All men are mortal," where all applies to each and 
every one of a specified kind although the singulars are not 
capable of enumeration. That "all" has these four meanings is a 
warning against using words as a clew to logical form apart from 
their context in inquiry. 

I now come to the topic of measurement by enumeration. A 
measured collection is identical with the kind of collection just 
said to have the property of totality in contrast with a merely num- 
bered aggregate. In the latter, subject-matter sets no limits, and 
consequently fails to prescribe a whole. Measured collections in- 
volve (1) limits from which to which; (2) something specified as a 
unit for counting; and (3) progressive accumulation of these units 
until the limit ad quern is reached. The word accumulation as here 
used involves something different from the aggregation found in the 
merely numerical set. When we measure the cubic capacity of a 
liquid container the successive addition of units is cumulative be- 
cause it progressively tends toward a limit. Even if we were able 
to count the number of drops of water that are contained, we 
should have at most simply an aggregation; as if it just happened 
there are so many drops — no less, no more. 

The cumulative aspect in genuine collective propositions signifies 
that such propositions depend upon some principle of arrangement 
or order which is derived from the involved means-consequences 
relation. Suppose, for example, that there are a number of ship- 
wrecked persons in a boat. The number is definite; and there is a 
definite amount of food and water on board, and the distance from 
land is also approximately known. The length of stay on board, 



210 THE STRUCTURE OF INQUIRY 

the distance from a ship that might rescue them, weather-condi- 
tions, etc., are, however, indeterminate, depending upon con- 
tingencies that cannot be accurately determined. Food and water 
are measured not just for the sake of enumeration but as a means of 
allotment, of distribution. Were there a store of food and water 
at hand that would last beyond the remotest date that could be set 
for rescue there would be no point in measuring. In the Garden 
of Eden it may be presumed that waste and stringency were both 
impossible. And in a similar situation no end is served by proposi- 
tions as to quantity. But in cases of excess and deficiency, de- 
termined to be such by reference to an end to be reached as a 
limit, apportionment is necessary if conduct is to be intelligent. 
Allotting, meting out, involves a principle of distribution, and this 
principle controls the subordinate operation of counting. There 
must be enough if the end is to be attained and just enough in 
the interest of economy and efficiency. 

The illustrations have been taken from the field of common 
sense, of situations of use-enjoyment. In this domain, control by 
the qualitative is most clearly evident. Indeed, as was indicated 
earlier, common sense propositions of quantity are likely to be 
themselves semi-qualitative. Emergence from this state was 
probably a slow historic process, being produced by exigencies of 
technology, exchange and science. The word few, for example, is 
derived from a root meaning poor; many from a root meaning 
abundance, fullness. While physical science depends upon meas- 
urement by means of enumerated homogeneous units, it is equally 
true of it that counting is for the sake of measuring and that 
measuring is controlled by the problem set by some qualitative 
situation, as one limit, and the objective consequence of a resolved 
situation as the other limit. Mere counting and mere measuring are 
childish (that is, immature) imitations of scientific procedure. 

The homogeneous units that are required for numerically de- 
terminate measurement are fixed first in the case of bodies ex- 
tended in space. An object that fills a span or stretch can be 
readily marked off into sub-spans or sub-stretches of approximately 
equal extent. Enumeration of these smaller intervals as units 
measures the extent of the larger body. The span of the hand, the 
pace in walking, were presumably the first such units evolved. A 



QUANTITY AND MEASUREMENT 211 

string can be doubled and redoubled and knots made at required 
points. By the use of a string knotted at approximately equal 
intervals notches can be cut in a stick, and the stick placed against 
some object. The length of the latter is measured by counting the 
number of notches in the superimposed rod as far as its extent and 
that of the object have the same ends or limits. The relatively 
qualitative long and short are refined into terms of so long or so 
short. Until the rise of geometry, however, the problem of com- 
plete reduction of the qualitative to quantitative relation was not 
solved — or even seen to be a problem. For the equality of in- 
tervals of the string and rod remained, after all, a matter of qualita- 
tive appraisal since it was conditioned by direct sensory-motor 
processes. 

The measurement of discrete objects is the case that on its face 
comes closest to being not a case of measuring but of mere count- 
ing. One counts the number of chairs in the room; the shepherd 
counts the sheep in his flock; a man counts the number of bills or 
coins in his pocketbook. But if there is no end-in-view in the 
counting (in which case there is no measuring and weighing) such 
counting is like that of children who, after they have learned to 
count, count for the fun of it — and even then there is some 
limiting object, like seeing if they can count up to a million. The 
shepherd counts in order to see if his flock is "all there"; if it is 
increasing or decreasing, etc. A man keeps track of his funds be- 
cause he has something to do with them, etc. More important is 
the fact that mere physical separation is not the ground of count- 
ing in the cases mentioned, provided "mere" means apart from 
consequence to be effected. So-called numerical identity is not 
something given to inquiry but is determined in inquiry. A 
book is the unit for one problem and purpose; a page for another; 
perhaps even a word or a letter is the unit as means to another 
end. A library, a whole set of books, may thus be the unit that has 
"numerical identity." The materials that appear in propositions as 
(numerical) identities are determined, like all other identifications, 
for and by operational use in solving some problem. 

A derived but ultimately more important mode of measurement 
has for its object increase and decrease in changes which ex- 
istentially are continuous — intensive as distinct from extensive 



212 THE STRUCTURE OF INQUIRY 

quantity. That a body is getting colder or warmer, is moving at 
greater or less speed, (or in general is tending toward a contrary 
quality) are comparisons expressing vague qualitative measure- 
ments that can be made on the basis of ordinary observations. The 
problem of converting these qualitative estimates into definite, that 
is to say, numerical form, involves overcoming difficulties that do 
not exist in the case of extended magnitudes. Continuous change 
of quality does not lend itself to division into homogeneous units, 
since by description the quality is continuously becoming heter- 
ogeneous to what it was. From the standpoint of the content of 
Greek science, with its disparaging view of change, all that was 
necessary was to classify the diverse kinds of qualitative change that 
occurred; as from warm to cold, wet to dry, soft to hard, up to 
down, and the reverse. In classic science it thus sufficed to say that 
all qualities of sense-perception change between opposite limits; 
cold and only cold is that which becomes warm and so on. There 
was no need for measurement and hence none for units by which to 
measure. 

The concept of series is not found in Greek science or logic. It 
did not appear until change was found capable of reduction, for 
the purpose of instituting controlled comparisons, to motion, and 
was thereby found capable of measurement in terms of homogene- 
ous units of space and time. Then the theory of celestial mechanics 
became for a time the model for all scientific descriptions and ex- 
planations. The problem set to inquiry was that of translating con- 
tinuous change of quality with which qualitative measurements can 
deal only in terms of intensive degree (more-less, least-most) into 
numbered extent, direction, velocity and acceleration of motion 
correlated with numbered units of duration. 

The problem was met by devices which permitted continuous 
qualitative change to be placed in functional correspondence with 
continuous extended stretches marked off into discrete homo- 
geneous units that can be counted. By the use of, say, a mercury 
thermometer, changes in the intensity of heat, which are not 
directly comparable with one another, are rendered comparable 
with fixed units of extension — fixed, that is, as far as other condi- 
tions can be kept constant. A numerical degree of temperature is 
a unit or sum of units of heat or cold indirectly. In itself it is the 



QUANTITY AND MEASUREMENT 213 

interval between two lines on a scale in which there is a column 
marked off on a glass tube containing, say, mercury. Change in 
temperature is measured by counting the number of such intervals 
and their fractional parts that are traversed by the enclosed 
mercury during a given time — which in turn is measured by a 
similar device in which the movement of an index or hand over a 
number of equally extended intervals on a dial or face yields 
enumerable units. The device is practicable because of the "law" 
of expansion and contraction of mercury, air or alcohol, with 
changes of temperature, conditions of pressure being maintained as 
constant as possible. The difference between immediate qualities 
of heat and cold is thus entirely eliminated, "absolute" or zero 
temperature being the point at which molecules cease to change 
position or move. The relation, or ratio, of qualitative changes 
to one another is thus determined through a proportion of which 
the other terms are the ratio which changes of position bear to one 
another, 2 

All of three types of comparison-measurement that have been 
discussed involve the operation of matching. In the first case, a 
certain extent of a rod is matched against an extent of a piece of 
cloth, side of a room, linear dimension of land, etc., etc. Measure- 
ment in the second case is made possible because objects can be 
matched against other objects taken as symbols — such sounds and 
marks, for example, as the numerals and figures one, two, three, 
four, etc. A word still in use, namely digits, suggests that the 
objects counted were first matched against toes and fingers. Al- 
though the latter are themselves existential, they are so when used 
in counting in the representative sense of sounds, and marks on 
paper, in linguistic communication. Toes and fingers as thus used 
are as symbolic as are the marks: 1, 2, 3, 4, etc. In the third case, 
changes in a continuum of change are matched against extended in- 
tervals, like those upon a glass tube or clock-face. In the first and 
third cases alike there is, in addition, a matching against syrnbols, 
such as are characteristic of the second case. The use of linguistic 
symbols, of mm&yvr-names, is the invention which permitted quan- 

2 The numerical determination of intelligence quotients will, for example^ be- 
come scientifically significant in the degree with which they can be definitely 
correlated with other specified changes. By themselves they simply set a problem. 



214 THE STRUCTURE OF INQUIRY 

tity and number to become objects of independent or mathematical 
investigation. For the relations of symbols to one another in a 
meaning-symbol system can be examined on their own account, 
independent of the relations existential objects and changes sustain 
to one another. 3 

Matching or correspondence in some form is thus the basic 
operation in all propositions in which determination of quantity, 
having existential reference, appears. This fact explains the sense 
in which number and magnitude are relational. The relation in- 
volved is complex. For example, suppose a stick is measured off 
into twelve equal intervals. It can then be affirmed that the rod is 
twelve such intervals long and that each interval is one-twelfth as 
long as the entire stick. But if the matter ended here, there would 
be no measurement. The propositions are not only circular but 
trivial. The rod and its subdivisions become a measure only when 
applied to other objects so that the rod and its intervals are matched 
against differences of interval in these other things. Until a foot- 
rule is used to measure other things it is not a rule, but merely a 
stick that happens to be notched or lined in a certain rather curious 
fashion. Even when one foot-rule or yard-stick is compared with 
another, there is, as such, no measurement, but only a check upon 
the accuracy of the measuring capacity of one or other or both. 

The standard meter is a bar of platinum kept under as constant 
conditions of temperature and pressure as possible in the city of 
Paris. But if that were the whole of the story, the word meter 
would not have the connection with measuring it actually has. By 
itself the bar is just a particular bar and nothing else; it is neither 
a standard of measurement nor is itself measured. It is a measure 
of length because (1) all other rods of a meter's length in use any- 
where in the world may be checked by being matched against it, 
and (2) because, and only because, these other rods are themselves 
used in matching still other things. It is just as true that the length 
of the bar of platinum (or any other measuring rod) is determined 
by its application in measuring cloth, walls, sides of fields, etc., 
as that the length of the latter is determined by comparison with it. 

3 See, ante, pp. 54, 110. Discussion of the relations existing among symbols as 
such takes us out of the field of number and magnitude that have direct existential 
reference into the domain of mathematics. Hence it is no part of the subject- 
matter here considered. It is taken up in Chap. XX. 



QUANTITY AND MEASUREMENT 215 



In short, when we apply the word measure to pounds, gallons, 
yards, etc., "measure" is an elliptic expression for means of 
measuring. Apart from operational use, the fact that pounds are 
relative to one another and to ounces and tons, has no measuring 
import. Moreover, foot and yard are not measures just because 
they can be matched against such qualitative objects as pieces of 
cloth (themselves qualitatively unlike), rolls of paper, boards, 
roads, fields, but are measures because this latter matching enables 
these other unlike qualitative things to be indirectly compared 
with respect to one another — just as, for example, matching dol- 
lar bills against a bushel of wheat would be of trivial importance if 
the matching of the bills against books, railway travel, groceries 
and houses did not enable indirect measurements or calculations to 
be undertaken about the values in exchange of these other things in 
relation to one another. The negation of quality or indifference to 
it which is sometimes ascribed to quantity and number (and a 
ground made for their disparagement) is not final but, on the 
contrary, positive means for controlled construction of new ob- 
jects and institution of new qualities. Just as a piece of paper, 
enacted by law into legal tender, is a means for comparing values in 
exchange of things qualitatively unlike, thus promoting and con- 
trolling new transactions with qualitative objects — so science 
renders things qualitatively unlike (as sounds and colors, pressures, 
light and electricity) comparable with one another, in such ways 
that controlled interchanges are capable of being brought about. 4 
What has been said has a definite bearing upon so-called stand- 
ards of value or more properly of valuation. It contradicts the 
notion that there are some entities that are standards "absolutely," 
that is, in themselves. 5 In the case of the platinum bar mentioned 
above no one would suppose that it is a standard measure of length 
because of some inherent property of absolute length. But in 
discussion of art, morals, economics and law it is a fairly usual as- 
sumption that critical evaluative judgments are impossible unless 
there is a standard of values which is such because of its own in- 

4 The ontological hypostization of a method, an instrumentality, of inquiry used 
to effect objective consequences, into something ontological, is the source of the 
mechanistic metaphysics of "reality." 

5 This notion is a twin of the notion of ends-in-themselves already criticised; 
see pp. 167-8. 



216 THE STRUCTURE OF INQUIRY 

herent constitution and properties. In economics it has been a 
fairly common assumption that gold is a standard measure of the 
value of other things because of its own "intrinsic" value. This 
idea appears almost always when paper money is denied the 
capacity to serve as a standard. Instead of a comparison of the 
capacity of gold and paper money to serve as standards on the 
ground of actual consequences operationally produced by their 
respective applications in determining exchange, an alleged absolute 
or "intrinsic" value in the case of gold is appealed to. 

In morals, it is a common assumption that the fairness of particu- 
lar actions cannot be determined unless there is some absolute 
standard with which they may be compared. The true and the 
beautiful are similarly hypostatized. But in fact, we institute 
standards of justice, truth, esthetic quality, etc., in order that 
different objects and events may be so intelligently compared ivkh 
one another as to give direction to activities dealing with concrete 
objects and affairs: — exactly as we set up a platinum bar as a 
standard measurer of lengths. The standard is just as much subject 
to modification and revision in one case as in the other on the basis 
of the consequences of its operational application. Belief in magic 
is not confined to primitive peoples. The superiority of one con- 
ception of justice to another is of the same order as the superiority 
of the metric system to the more or less haphazard set of weights 
and measures it has replaced in scientific practice, although not of 
the same quality. 

Yard and mile, ounce and pound, gill and gallon, are conceptual 
meanings of the same general type as common sense conceptions, 
which, as we have seen, are related to one another on socio-historic 
grounds. They are means of facilitating and executing all kinds of 
social transactions with reference to use and enjoyment. The 
metric system of measurements is rather of the type of the system 
of symbol-meanings which is framed on the basis of inter-relation 
and free translatability. The propositions that result from their 
application are still instrumental, although to a different end; in 
the latter case, that of facilitation of inquiry. Conceptions and 
principles that serve to measure or evaluate moral conduct and re- 
lations are logically of the same kind, and should be so treated in 
social practice. 



QUANTITY AND MEASUREMENT 111 

It should be pointed out, by way at least of anticipation, that, 
according to the principle expounded, space and time are in science 
not what we measure but are themselves results of measurements of 
objects and events, in the interest of objective determination of 
problematic situations. This fact has, in the context of present 
discussion, definite bearing on the relation of discrete and con- 
tinuous magnitude, as these are found in propositions having ex- 
istential reference. A unit of measurement is, when it is taken as 
a unit of measurement, discrete. But it is internally continuous 
whether it be a millimetre or a kilometer. What is taken as discrete 
in one functional use is used as continuous in resolution of another 
problem and conversely. The same principle applies in proposi- 
tions of temporal dates (discrete) and temporal durations (con- 
tinuities). Even if there are, existentially, indivisible discrete 
pulses of change such that each change comes as a unitary whole, 
nevertheless, (1) such pulses must have direction if they can be 
used in determination of change as continuous, and (2) they are 
units of temporal measurement only when they are taken and 
used as means of comparison and measurement. Direction is nec- 
essary because it is required to effect that overlapping which is 
characteristic of all gross and observed change, since the latter 
could not arise by laying discrete pulses of change end to end. 

These unitary pulses if they exist are as qualitative as is the 
bar of platinum referred to. They become units of magnitude 
only as they are functionally employed to connect into a unified 
scheme changes that by themselves are disparate and heterogeneous. 
Schematization of time as a straight line indefinitely extended in 
one direction may be useful for some purposes. But duration as it 
enters into an existential (non-mathematical) proposition has the 
thickness which is constituted by overlapping of sequential changes 
and by the fact that determination of any specific change re- 
quires reference to changes occurring contemporaneously. To 
say, for example, that a certain reign lasted from 1800 to 1830 
would have no meaning if the interval in question had no other 
content than this reign. 

It may be advisable to refer explicitly to the existential opera- 
tions involved in comparison-measurements. In the matching char- 
acteristic of common sense it takes the obvious form of scoring and 



218 THE STRUCTURE OF INQUIRY 

tallying, along with the activity of juxtaposing or superimposing. 
When the matching takes place by means of number-names, the 
names, even though they are but symbols, have to be pronounced 
or marked down, if counting is to be effected. Counting is as 
existential an operation as is whistling or singing. Calculations 
in scientific work may go on in the head as well as they may be 
written down on paper. But symbols as symbols do not have 
physical efficacy. They have to be existentially manipulated if 
calculation occurs. The habit of ruling out the existential acts of 
counting and calculation from the domain with which logic is 
concerned is simply another instance of the systematic neglect of 
operations, so characteristic of formalistic logic, a neglect which is 
due to the doctrine that propositions are merely enunciative or 
declarative of antecedent existence or subsistence. 

Finally, qualitative control of existential propositions of number 
and magnitude is relevant to the difference between unity and a 
unit. Only that is unified or a unity which is a qualitative whole. 
In the language employed earlier in this chapter, it has members but 
is not an aggregate nor a collection of parts. When a qualitative 
whole is internally conflicting the pervasive whole affects the 
quality of the conflict, just as a civil war is what it is because it is 
disruption of and within a unity of a nation or people. The con- 
flict can only be resolved and a new qualitative unified situation be 
produced by going outside the situation that is antecedently in 
existence so as to eliminate some of its factors and to introduce other 
new factors. Hence the necessity of comparison-contrast, which 
as we have seen is a name for the operations by which this elimina- 
tion and introduction are effected. Control of the operations 
performed is exercised by the intent of production of a new 
unified situation. Propositions are the means by which the intent 
is carried out. The means are economical and effective (as in the 
reaching of any objective consequence) in the degree in which 
comparison takes the form of measuring and weighing. Without 
results secured by these operations, means employed either fail to 
bring about the intended end or they produce more than is in- 
tended, thereby creating a situation that perhaps is more trouble- 
some and conflicting than the original one which the means used 
were intended to unify. Qualitative wholes as such are incom- 



QUANTITY AND MEASUREMENT 219 

mensurable, just because they are uniquely qualitative. But they 
are the limits or "ends" from which and to which propositions are 
means. As such limits they provide the criteria by which the 
relevancy and force of propositions of measurement, qualitative 
and quantitative, are measured. 



CHAPTER XII 

JUDGMENT AS SPATIAL-TEMPORAL 

DETERMINATION: NARRATION-DESCRIPTION 



"udgment is transformation of an antecedent existentially in- 
determinate or unsettled situation into a determinate one. 
As such, judgment is always individual in a sense in which 
individual is distinguished from both particular and singular, in 
that it refers to a total qualitative situation. In this sense there are 
no different kinds of judgment, but distinguishable phases or em- 
phases of judgment, according to the aspect of its subject-matter 
that is emphasized. 1 In the opening statement existential trans- 
formation is the point of emphasis. Existential subject-matter as 
transformed has a temporal phase. Linguistically, this phase is 
expressed in narration. But all changes occur through interactions 
of conditions. What exists co-exists, and no change can either 
occur or be determined in inquiry in isolation from the connection 
of an existence with co-existing conditions. Hence the existential 
subject-matter of judgment has a spatial phase. Linguistically, this 
is expressed in description. For purposes of analysis and exposition 
the two phases must be distinguished. But there is no separation 
in the subject-matter which is analyzed. Whatever exists in and 
for judgment is temporal-spatial. In a given proposition, either the 
temporal or the spatial aspect may be uppermost. But every nar- 
ration has a background which, if it were made explicit instead of 
being taken for granted, would be described; correspondingly, 
what is described exists within some temporal process to which 
"narration" applies. 

1 The two previous chapters have indicated, for example, that "quantity" and 
"quality" in judgment must be distinguished in discourse but that they cannot be 
separated. 

220 



NARRATION AND DESCRIPTION 221 

I. I begin with consideration of that phase of the development of 
judgment in which temporal considerations are dominant. Their 
simplest form is found in propositions about changing present 
existential subject-matter linguistically expressed through active 
verbs in the present tense. Examples are such observations as "The 
Sun is rising; it is growing brighter; the room is getting cold; he is 
coming closer; the clock is striking; the fire is dying down, etc." 
In such a proposition as, "He was here a few minutes ago but has 
now gone," the subject-matter is of the same kind, but the words 
"was" — "ago" and "has gone" make explicit a reference to the past 
that is involved in the first set of sentences but that is there a matter 
of understood context. For it is indispensable to note that a limit- 
ing reference to both past and future is present in every existential 
proposition. There is reference to a limit ab quo and ad qitem. 
Without this limitation, a change is not characterized or qualified. 
No mere flux can be noted, appraised or estimated. A change is 
characterized in terms of direction — fro?n something to something. 
"The sun is rising" — that is, it was below the horizon, but is now 
moving further and further above the horizon. Such propositions 
as "It is sweet or red" state (as has already been noted) either that 
something is becoming or has become a changed quality, or 
else that it has the capacity to change — to redden or sweeten — 
something else. 

The point just made has a fundamental importance for the 
theory of the temporal and historic phase of judgment which may 
not be apparent at first sight. For it signifies that the unitary 
subject-matter of every temporal proposition is a round, cycle, 
period, circuit, or hora. To judge is to render determinate; to 
determine is to order and organize, to relate in definite fashion. 
Temporal order is instituted through rhythms which involve 
periodicities, intervals, and limits; all of which are inter-involved. 
Absolute origins and absolute closes and termini are mythical. 
Each beginning and each ending is a delimitation of a cycle or 
round of qualitative change. A date, a moment or point of time, 
has no meaning except as such a delimitation. > 

That which exists is, as existent, indifferent to delimitation in 
respect to beginnings and endings. There are no absolute origina- 
tions or initiations or absolute finalities and terminations in nature. 



222 THE STRUCTURE OF INQUIRY 

The "from which" and "to which" that determine the subject- 
matter of any particular narration-description are strictly relative 
to the objective intent set to inquiry by the problematic quality of 
a given situation. Such an event as, say, daybreak is the initial 
limit of subject-matter in one problem; the terminal limit in an- 
other, and an intermediate event in still a third problem — as, for 
example, in a proposition about the diurnal rotation of the earth. 
Generalized measures of temporal sequences, (such as are desig- 
nated by the words second, minute, hour, day, year, century, 
period, epoch) stand for kinds of cycles which, like all measures, 
are procedural means of furthering and directing the inclusions- 
exclusions (affirmations-negations) by which determinate subject- 
matter of propositions is instituted. 2 

Since every change when it is subjected to inquiry is a round 
or cycle of events whose beginning and ending are determined by 
the indeterminate situation undergoing resolution (and hence are 
not absolute), every given change may be narrated in terms of an 
indefinite variety of included minor events as incidents, episodes or 
occurrences. To a layman a flash of lightning comes close to being 
an isolated instantaneous occurrence. A scientific account of it is a 
narration of a prolonged history of which the flash is one incident; 
with the growth of scientific knowledge the tale becomes longer. 
On the other hand, a mountain, which to the layman is a standing 
symbol of permanence, is to the geologist the scene of a drama of 
birth, growth, decay and ultimate death. Unless the difference 
between existential change as barely existential and as subject- 
matter of judgment is borne in mind, the nature of event becomes 
an inexplicable mystery. Event is a term of judgment, not of 
existence apart from judgment. The origin and development of 
the Appalachian Mountain Range is an event, and so is the loosen- 
ing and rolling of a particular pebble on a particular ledge on a 
particular foot-hill. There may be a situation in which the latter 
sort of episode is much more important in judgment than is the 
history of long duration: as, for example, when a rolling pebble is 

2 The above considerations have definite bearing upon the probability-function 
of all existential propositions. For selection of events as initial and terminal with 
respect to solution of a giv^n problem involves a risk which can never be com- 
pletely eliminated. It also has a definite bearing (taken up in Chap. XXIII) 
upon the category of causation. 



NARRATION AND DESCRIPTION 223 

the "cause" of a sprained ankle. In the story of the cyclical 
weathering of the mountain, the roll of the pebble would hardly 
be an event at all; it would be but a specimen, unnoted in itself, of 
a kind of thing that is significant only en masse. An event is, 
strictly, that which comes out; that which issues forth; the net 
outstanding consequence, the eventuation. It involves a teleologi- 
cal concept; it is capable of description-narration only in terms of 
a delimiting beginning, an interval and a termination. 

Propositions in which temporal connections enter explicitly into 
the formation of judgment may be conveniently considered under 
three heads: (1) Those about one's personal past, (2) those about 
special events not coming directly within one's own experience, 
and (3) consecutive historical narrations. 

1. Judgments of Recollection. These are often disposed of by 
attributing them directly to a faculty of memory. This procedure 
consists in giving a name to the fact that judgments about one's 
past and history are possible and actual, and then treating the fact 
as if it were a causal force. To affirm that I did a given thing 
yesterday, or that I was ill last month, is to form an appraisal of a 
temporal sequence. It differs from any other historical reconstruc- 
tion only in the fact that its subject-matter falls within my own 
biography. If the affirmation is grounded, it is mediated and hence 
depends upon evidential data instituted by observations. Like 
every mediated outcome, it is subject to error even though its 
subject-matter is something done or suffered five minutes ago. 
While in explicit linguistic statement the content of the proposi- 
tion is usually a particular deed or something undergone at a 
particular time in the past, the actual logical object is a course of 
events, one limit of which is the present while the other is what 
happened at the specified past time. 

The instance in question thus exemplifies the principle that a 
cycle or period is the object of every temporal proposition. Take 
the proposition "I went to Yonkers yesterday," or any other sen- 
tence about a particular act. On its face, it refers to an isolated 
occurrence. But "I" in this sentence has no meaning except as the 
/ of today and of yesterday and of the days which preceded. 
Moreover, the particular act mentioned has background and fore- 
ground. If it were not involved in a continuing course of exist- 



224 THE STRUCTURE OF INQUIRY 

ence, out of which it grows and to which it contributes, that is, if 
it were completely isolated and self -enclosed, neither assigned date 
nor "I" would have the slightest meaning. 

Some present state of affairs is always the occasion of the re- 
construction of the past event. But as a mere occasion, it has no 
logical standing. By some organic mechanism (of the general 
nature of the physical modification called habit) it calls out or 
"suggests" something not present. This suggested something as 
such also lacks logical status. It may be a whimsy or castle in the 
air, and, in any case, if what is suggested is immediately accepted, 
without inquiry and test, as representative of something in my past 
history, there may be a proposition in the outer form of linguistic 
expression but not in its logical status. For the affirmation is with- 
out ground — a fact that is celebrated as a virtue by those who im- 
pute it to an intuition of the "faculty" of memory, but who in 
reality take the product of the working of a psycho-physiological 
mechanism as a case of knowledge. In order to figure in a proposi- 
tion having logical character, the idea of a past event suggested by 
the associative mechanism has to be critically scrutinized. Did I 
really do thus and so? Or did I merely think of doing it? Or 
was it just something that I heard and that left a vivid impres- 
sion on me? Or perhaps it is something that I now wish I had 
done? 

Even those who hold that at least some "memory ideas" or 
"images" bring with them as part of themselves a tag to the effect 
that something corresponding to them actually happened in one's 
past experience, do not, nevertheless, go so far as to maintain that the 
idea or image brings the exact date of its occurrence with it. Since 
(1) the temporal place (date) of an occurrence in a sequential 
event is integrally involved in any recollection of one's past, and 
since (2) such temporal place, or date, is not an inherent part of 
what is suggested (since, that is, the suggested past event does not 
carry its date stamped upon it), the matter of the recollection is 
evidentially mediated; it is a matter of judgment. Its validity is 
as much dependent upon the material used as evidential data as is 
that of an inference about some event wholly outside of one's 
own personal past. 

Dating, moreover, is nothing absolute. It depends upon con- 



NARRATION AND DESCRIPTION 225 

necting a particular occurrence with other events coming before 
and after in such a way that taken together they constitute a 
temporal series or history. If I say that "I was at home at five 
o'clock yesterday," I am in fact constructing as an object of 
grounded belief a sequential course of events. "Yesterday" has 
no significance save in connection with today, the day-before- 
yesterday and a series of tomorrows. "Five o'clock" has no sig- 
nificance save in connection with four and six o'clock, and so on. 
The problem presented by the enduring situation undergoing de- 
termination gives the date fixed upon its crucial significance. Were 
the facts as isolated and independent in existence as they appear 
to be in a sentence when the latter is separated from context, the 
latter would have no more meaning than if uttered by a parrot, 
and were the sentence uttered by a phonograph, its meaning would 
be fixed by the context, say of the story or dramatic reproduction 
in which it appears. Here, as in so many cases, the context is 
linguistically suppressed just because it is taken for granted. 

If a memory-affirmation is questioned either by another or by 
one's self it is supported by making explicit the temporal con- 
textual sequence. "At half past four I was leaving my office and 
it takes me just about half an hour to get home; I came straight 
back and remember looking at the clock as I came in and then I 
picked up the evening paper and was reading when so and so came 
in," and so on. Satisfactory as such a consecutive reconstruction 
may be for most practical purposes, it does not logically suffice. 
For these other incidents are also matters of recollection and them- 
selves demand the same kind of grounded substantiation as the 
original judgment of recollection. It is at this point that the ref- 
erence to objective evidential confirmation comes into play. The 
consistency of an account of an event alleged to have occurred 
with accounts of other specified events alleged to have occurred 
before and after is good as far as it goes, but is subject to the 
limitations that affect all cases of merely internal consistency. 
Paranoiac reconstructions of the past often have marvellous inter- 
nal consistency. In crucial instances, such as sometimes present 
themselves, for example, in law courts, external evidence of docu- 
ments, direct observations of other persons, etc., is imperatively 
demanded. Whenever there is reason to suspect collusion or com- 



226 THE STRUCTURE OF INQUIRY 

mon interest in establishing belief in a fictitious state of affairs, 
an even more external kind of evidence, more external in being 
independent of any personal element, will alone logically suffice — 
although, of course, in many cases we have to act upon evidence 
that falls far short of complete logical conclusiveness. 

In other words, such judgments, like those about all existential 
matters, have probability, not "certainty." Hence the actions 
that are performed in consequence of accepting them are not 
logically ex post facto or mere practical appendages to a com- 
pleted judgment. They are operations that provide additional 
evidence, which confirms, weakens, or in some way modifies, the 
provisionally accepted appraisal. Suppose I am in doubt whether 
I mailed a certain letter after writing it. I assume temporarily 
that I did mail it, and perform the operation of waiting for the 
reply which it called for. The consequence serves to determine 
the correctness of my assumption: I receive a reply or do not 
receive it. Or, I fear strongly that I did not mail the letter. I 
perform the operation of looking through all the places where I 
might probably have laid it. Not finding it I still am unwilling 
to accept as conclusive the idea that I mailed it. I write another 
letter inquiring to make sure whether it was mailed or not. What 
these illustrations bring out is that the consecutive qualitatively 
continuous history which is constructed is not confined to the past. 
Events occurring in the future stand in such relations of continuity 
to those that have occurred and those now occurring that they 
serve as evidential matter for testing provisional appraisals of recol- 
lection about what we have done and what has happened to us in 
the past. 

A marked breach of continuity in the sequence of future or 
ensuing events with what we suppose happened in the past is 
enough, as a rule, to make us believe our belief invalid if not 
imaginary. On the other hand, the recurrent frequency with 
which subsequent events bear out reliance upon reconstructive 
temporal judgments gives us pragmatic confidence in their general 
dependability. Consequences of the method in the continuity of 
inquiry are the ground upon which data are relied upon when they 
themselves are materially inadequate. This confidence causes us 
as a matter of routine to act upon their accuracy without sub- 



NARRATION AND DESCRIPTION 227 

mitting them to special logical tests. The very cases which 
superficially viewed give rise to the belief that recollections of 
one's past are not mediated judgments, but are cases of "immediate 
or intuitive knowledge," are just the ones which, when they are 
closely examined, show that they are instances of construction of 
extensive durational sequences of events. Upon the whole, the 
trustworthiness of our reconstructions of personal past experience 
is so repeatedly confirmed by the course of ensuing events that we 
come to depend upon them without applying special tests. Only 
in cases of crucial doubt do we resort to the latter. 

It may perhaps seem that much time has been spent in arguing a 
point that is quite obvious on its face, or that if not obvious, is in 
any case not a matter of much importance. Such is not the case. 
For the point that every temporal proposition is a narrative propo- 
sition means that the proposition is about a course of sequential 
events, not about an isolated event at an absolute point in time. 
This thesis is of such fundamental importance that it is necessary 
to establish it beyond reasonable doubt. The simplest instance is 
that of recollection. Since, as a result of borrowing from un- 
criticized psychological doctrine, the idea has become current that 
recollection is a case of "immediate" re-instatement of the past, it 
possesses crucial logical significance. 

The net conclusion of the foregoing discussion will, accord- 
ingly, be formally set forth. A continuous course or round of 
events, a period marked by limits and interval, is the subject- 
matter undergoing determinate settlement in propositions of recol- 
lections of a personal past. In such determinations provisional 
judgments (of the nature of appraisals or estimates) have to be 
made about both present objects or events and past occurrences. 
Such judgments are not final and complete. They are the means 
by which conclusive and complete judgment about an entire 
course of sequential events, a history, extending from the past 
through the present into the future, is groundedly instituted. It is 
for the sake of resolving a total qualitative situation that the pro- 
visional judgments about past and present events — in the temporal 
sense of past and present— are made. When it is said that judg- 
ments of recollection are not complete in themselves but are in- 
strumental means of requalifying a present situation, otherwise 



228 THE STRUCTURE OF INQUIRY 

problematic, the word "present" does not mean a temporal event 
that may be contrasted with some other event as past. The situa- 
tion that I am determining when I attempt to decide whether or 
not I mailed a certain letter is a "present" situation. But the pres- 
ent situation is not located in and confined to an event here and 
now occurring. It is an extensive duration, covering past, present 
and future events. The provisional judgments that I form about 
what is temporally present (as for example in going through my 
pockets now) are just as much means with respect to this total 
present situation as are the propositions formed about past events 
as past and as estimates about ensuing events. 3 

2. Judgments of Events Outside of Personal Recollections. We 
constantly make judgments which reconstruct past scenes that are 
so completely outside of personal experience that there is no pos- 
sibility of applying the doctrine of immediate or self-evident 
knowledge. A man is found dead under circumstances which 
prima facie provide no evidence as to the time and manner of his 
death. There are, however, conditions capable of observation. 
Analytic examination, employing available instruments and tech- 
niques, are brought into play. Present data are thus obtained as 
the basis of inference as to what took place in the past. Medical 
examination supplies data from which inference fixes approxi- 
mately the time of the death and something concerning its im- 
mediate conditions; it happened, say, about eight hours before from 
a bullet fired from a revolver of a certain calibre, etc. The bare 
data do not, of themselves, provide these conclusions. The in- 
ferential conclusions drawn are an interpretation of directly ob- 
served facts mediated by conceptions drawn from prior experience; 
these conceptions being logically adequate in the degree that past 
experience has been critically analyzed. Moreover, the proposi- 
tions that formulate the inferred conclusions are clearly interme- 
diary, not final. 

The data are such, we will say, as to preclude the possibility or 
idea of suicide. They suggest murder, but do not signify it. The 
man may have been shot accidentally or in self-defense during a 
struggle. Other investigations look for evidences of robbery; for 

3 The ambiguity of the term "present"— like that of "given"— has already been 
noted. See, ante, pp. 124-5. 



NARRATION AND DESCRIPTION 229 

men who had a motive for the act; for witnesses who may have 
heard a shot fired or seen a struggle, etc. When the dead body is 
identified, there is investigation of the person's movements when 
alive; whether he carried money; his enemies, previous threats 
against him, etc. Since it is not here a matter of writing a detec- 
tive story, I only need to point out that evidential data consist 
(1) of facts that are now observable, stated in propositions that 
refer to temporally contemporaneous facts, and (2) of data derived 
from recollections of earlier observations. Given these proposi- 
tions, the problem is to weave them into a grounded conclusion 
that the man in question met his death at the hands of another 
person at a certain time and under such circumstances as to bring 
the act under the legal conception of murder of the first degree. 
(For no matter how detailed are the material data they constitute 
a problem of this general logical type.) Solution of such a prob- 
lem is impossible save upon the postulate that the subject-matter 
under inquiry is that of a temporal course of sequential events and 
upon the condition that the material in question satisfies this 
postulate. There are propositions on the one hand about things 
now observable; as, for example, there is no legal ground for ac- 
cusing any one unless there is a corpus delicti On the other hand, 
there are propositions about events that happened in the past. But 
neither set of propositions has probative force unless temporal con- 
tinuity can be reasonably established between their respective 
subject-matters. It is the course of events constituting this history 
that is the object of logical determination. The propositions that 
are accumulated about past facts and facts now observable are but 
means to the formation of this historic narrative judgment. In 
themselves they are so many separate items. They are not com- 
plete and final. Moreover, the history under determination ex- 
tends into the future. Something to ensue hangs upon the 
detection and conviction of a given person as the murderer: execu- 
tion or imprisonment. 

Take the case of a man who after a certain lapse of time pre- 
sents himself as the legal claimant to an estate of a dead man, the 
estate having in the meantime been awarded to another person as 
the heir. The case, we will assume, is such that if the claimant is 
the man he claims he is, there is no doubt on the legal side that he 



230 THE STRUCTURE OF INQUIRY 

is the one who is entitled to the estate. The problem is one, in 
short, of identification. A proposition to the effect that the claim- 
ant is or is not so-and-so, say Tichborne, is thus required to de- 
termine the matter in dispute, while this proposition does not 
represent the object of final determination. It is intermediate and 
instrumental to a judgment about the conclusive disposition of the 
estate. The proposition of identification operates as an instrumen- 
tality, moreover, only by instituting historic continuity or ab- 
sence of such continuity between the given individual about whose 
past certain propositions are offered, and the individual about 
whom propositions are formed on the basis of contemporary ob- 
servations. Here, as in our previous case, propositions have to be 
formed about contemporary facts and past events. But neither 
set of propositions proves anything nor do both of them together 
until they are filled out by propositions which bring their contents 
into temporal continuity with one another. Furthermore, a future 
consequence, the final disposition of the estate, is involved. This 
outcome also is historical, being the completion of a course of 
events. Taken in isolation, it is no more the object of determina- 
tion than is the subject-matter constituted by past events or is that 
constituted by contemporary observable date: — such as, physical 
constitution, appearance, birthmarks, etc. 

What is true in the two instances just mentioned is true of all 
judgments of events in their temporal qualifications. There is no 
such thing as judgment about a past event, one now taking place, 
or one to take place in the future in its isolation. The notion 
that there are such judgments arises from taking propositions that 
are indispensable material means to a completely determined situa- 
tion as if they were complete in themselves. 

3. Judgments Recognized to be Historical. The distinctively 
logical importance of the conclusions so far reached appears even 
more clearly when we come to the theme of historical judgments 
in the ordinary sense of history. In the latter case, there is no such 
need to dwell upon the issue of temporal continuity of subject- 
matter as there was in the topics that have been discussed. For 
history is admittedly history. The logical problem involved now 
takes a more restricted form: Given temporal continuity, what is 
the relation of propositions about an extensive past durational 



NARRATION AND DESCRIPTION 231 

sequence to propositions about the present and future? Can the 
historical continuum involved in admittedly historical propositions 
of the past be located in the past or does it reach out and include 
the present and future? There are of course, many technical 
methodological problems that have to be met by the historian. 
But the central logical problem involved in the existence of 
grounded judgment of historical subject-matter is, I take it, that 
which has just been stated. What conditions must be satisfied in 
order that there may be grounded propositions regarding a sequen- 
tial course of past events? The question is not even whether 
judgments about remote events can be made with complete war- 
rant much less is it whether "History can be a science." It is: 
Upon what grounds are some judgments about a course of past 
events more entitled to credence than are certain other ones? 

That evidential data for all historical propositions must exist 
at the time the propositions are made and be contemporaneously 
observable is an evident fact. The data are such things as records 
and documents; legends and stories orally transmitted; graves and 
inscriptions; urns, coins, medals, seals; implements and ornaments; 
charters, diplomas, manuscripts; ruins, buildings and works of art; 
existing physiographical formations, and so on indefinitely. Where 
the past has left no trace or vestige of any sort that endures into 
the present its history is irrecoverable. Propositions about the 
things which can be contemporaneously observed are the ultimate 
data from which to infer the happenings of the past. This state- 
ment, in spite of its obviousness, needs to be made. Although it is 
taken for granted as a matter of course by those who work with 
source material, readers of the works which historians compose on 
the basis of available source-material are likely to suffer from an 
illusion of perspective. Readers have before them the ready-made 
products of inferential inquiry. If the historical writer has dra- 
matic imagination, the past seems to be directly present to the 
reader. The scenes described and episodes narrated appear to be 
directly given instead of being inferred constructions. A reader 
takes conclusions as they are presented by the historian to be di- 
rectly given almost as much as he does in reading a well con- 
structed novel. 

Logical theory is concerned with the relation existing between 



232 THE STRUCTURE OF INQUIRY 

evidential data as grounds and inferences drawn as conclusions, 
and with the methods by which the latter may be grounded. With 
respect to logical theory, there is no existential proposition which 
does not operate either (1) as material for locating and delimiting 
a problem; or (2) as serving to point to an inference that may be 
drawn with some degree of probability; or (3) as aiding to weigh 
the evidential value of some data; or (4) as supporting and testing 
some conclusion hypothetically made. At every point, exactly 
as in conducting any inquiry into contemporary physical condi- 
tions, there has to be a search for relevant data; criteria for selec- 
tion and rejection have to be formed as conceptual principles for 
estimating the weight and force of proposed data, and operations 
of ordering and arranging data which depend upon systematized 
conceptions have to be employed. It is because of these facts that 
the writing of history is an instance of judgment as a resolution 
through inquiry of a problematic situation. 

The first task in historical inquiry, as in any inquiry, is that of 
controlled observations, both extensive and intensive — the collec- 
tion of data and their confirmation as authentic. Modern his- 
toriography is notable for the pains taken in these matters and in 
development of special techniques for securing and checking data 
as to their authenticity and relative weight. Such disciplines as 
epigraphy, paleography, numismatics, linguistics, bibliography, 
have reached an extraordinary development as auxiliary techniques 
for accomplishing the historiographic function. The results of 
the auxiliary operations are stated in existential propositions about 
facts established under conditions of maximum possible control. 
These propositions are as indispensable as are those resulting from 
controlled observation in physical inquiry. But they are not final 
historical propositions in themselves. Indeed, strictly speaking 
they are not in their isolation historical propositions at all. They 
are propositions about what now exists; they are historical in their 
•function since they serve as material data for inferential construc- 
tions. Like all data they are selected and weighed with reference 
to their capacity to fulfill the demands that are imposed by the 
evidential function. 

In consequence, they are relative to a problem. Apart from 
connection with some problem, they are like materials of brick, 



NARRATION AND DESCRIPTION 233 

stone and wood that a man might gather together who is intend- 
ing to build a house but before he has made a plan for building 
it. He ranges and collects in the hope that some of the materials, 
he does not yet know just what, will come in usefully later after 
he has made his plan. Again, because of connection with a prob- 
lem, actual or potential, propositions about observed facts corre- 
spond strictly with conceptual subject-matter by means of which 
they are ordered and interpreted. Ideas, meanings, as hypotheses, 
are as necessary to the construction of historical determinations 
as they are in any physical inquiry that leads to a definite conclu- 
sion. The formation of historical judgments lags behind that of 
physical judgments not only because of greater complexity and 
scantiness of the data, but also because to a large extent historians 
have not developed the habit of stating to themselves and to the 
public the systematic conceptual structures which they employ in 
organizing their data to anything like the extent in which physical 
inquirers expose their conceptual framework. Too often the con- 
ceptual framework is left as an implicit presupposition. 

The slightest reflection shows that the conceptual material em- 
ployed in writing history is that of the period in which a history 
is written. There is no material available for leading principles 
and hypotheses save that of the historic present. As culture 
changes, the conceptions that are dominant in a culture change. 
Of necessity new standpoints for viewing, appraising and ordering 
data arise. History is then rewritten. Material that had formerly 
been passed by, offers itself as data because the new conceptions 
propose new problems for solution, requiring new factual material 
for statement and test. At a given time, certain conceptions are 
so uppermost in the culture of a particular period that their ap- 
plication in constructing the events of the past seems to be justified 
by "facts" found in a ready-made past. This view puts the cart 
before the horse. Justification if it is had proceeds from the 
verification which the conceptions employed receive in the pres- 
ent; just as, for example, the warrant for the conceptual structures 
that are employed to reconstruct what went on in geological ages 
before the appearance of man or indeed of life on the earth, is 
found in verified laws of existing physical-chemical processes. 
For example, the institution of paleolithic, neolithic and bronze 



234 THE STRUCTURE OF INQUIRY 

ages of "prehistoric times," with their subdivisions, rests upon a 
knowledge of the relation between technological improvements 
and changes in culture which is obtained and verified on the 
ground of contemporaneous conditions. Since differences in, say, 
the refinement of quality of the edges of stone implements do not 
bring their relative dates engraved upon them, it is clear that their 
use as signs of successive levels of culture is an inference from 
conceptions that are warranted, if at all, by facts that now exist. 
An extensive doctrinal apparatus is required in order to correlate 
with one another such varied data as fossil survivals, artefacts, 
ashes, bones, tools, cave-drawings, geographical distributions, and 
the material that is drawn from study of existing "primitive" 
peoples. Yet without these extensive correlations the reconstruc- 
tion of "prehistoric" times could not proceed. 

Recognition of change in social states and institutions is a pre- 
condition of the existence of historical judgment. This recogni- 
tion in all probability came about slowly. In early days it was 
confined, we may suppose, to emergencies so great that change 
could not escape notice: such as mass migrations, plagues, great 
victories in war, etc. As long as these changes were supposed to 
constitute isolated episodes, history cannot be said to have emerged. 
It came into existence when changes were related together to con- 
stitute courses, cycles or stories having their beginnings and clos- 
ings. Annals are material for history but hardly history itself. 
Since the idea of history involves cumulative continuity of move- 
ment in a given direction toward stated outcomes, the fundamental 
conception that controls determination of subject-matter as his- 
torical is that of a direction of movement. History cannot be 
written en masse. Strains of change have to be selected and ma- 
terial sequentially ordered according to the direction of change 
defining the strain which is selected. History is of peoples, of 
dynasties; is political, ecclesiastical, economic; is of art, science, 
religion and philosophy. Even when these strains are woven to- 
gether into an effort to construct a comprehensive strand that 
covers a movement taken to be relatively complete, the various 
strains must first be segregated and each followed through its 
course. 

From acceptance of the idea that inferential determinations of 



NARRATION AND DESCRIPTION 235 

history depend upon prior selection of some direction of move- 
ment, there follows directly a consideration of basic logical im- 
portance. All historical construction is necessarily selective. Since 
the past cannot be reproduced in toto and lived over again, this 
principle might seem too obvious to be worthy of being called im- 
portant. But it is of importance because its acknowledgment com- 
pels attention to the fact that everything in the writing of history 
depends upon the principle used to control selection. This prin- 
ciple decides the weight which shall be assigned to past events, 
what shall be admitted and what omitted; it also decides how the 
facts selected shall be arranged and ordered. Furthermore, if the 
fact of selection is acknowledged to be primary and basic, we are 
committed to the conclusion that all history is necessarily written 
from the standpoint of the present, and is, in an inescapable sense, 
the history not only of the present but of that which is con- 
temporaneously judged to be important in the present. 

Selection operates in a three-fold way. The first selection in 
order of time is made by the people of the past whose history is 
now written, during the very time when they lived. Herodotus 
wrote, he said, "in order that the things which have been done 
might not in time be forgotten." But what determined his selec- 
tion of the things which should not be forgotten? To some minor 
extent, doubtless, his personal preferences and tastes; such factors 
cannot be wholly excluded in any case. But if these factors had 
been the only or main agency, his history would itself have soon 
been forgotten. The decisive agency was what was prized by the 
Athenian people for whom he directly wrote; the things this people 
judged worthy of commemoration in their own lives and achieve- 
ments. They themselves had their appraisals of worth which were 
operating selectively. The legends they transmitted and the things 
they forgot to retell, their monuments, temples and other public 
buildings, their coins and their grave-stones, their celebrations and 
rites, are some of the selective evaluations they passed upon them- 
selves. Memory is selective. The memories that are public and 
enduring, not private and transitory, are the primary material 
within which conscious and deliberate historians do their work. 
In more primitive peoples, folklore, implements, enduring relics, 
serve, in spite of the accidental ravages of time, the same function 



236 THE STRUCTURE OF INQUIRY 

of self-appraisal that is passed by living peoples upon their own 
activities and accomplishments. 

The historiographer adds a further principle of selection. He 
elects to write the history of a dynasty, of an enduring struggle, 
of the formation and growth of a science, an art or a religion, or 
the technology of production. In so doing, he postulates a career, 
a course and cycle of change. The selection is as truly a logical 
postulate as are those recognized as such in mathematical proposi- 
tions. From this selection there follow selective appraisals as to 
(1) the relative weight and relevancy of materials at his disposal 
and (2) as to the way they are to be ordered in connection with 
one another. There is no event which ever happened that was 
merely dynastic, merely scientific or merely technological. As 
soon as the event takes its place as an incident in a particular his- 
tory, an act of judgment has loosened it from the total complex of 
which it was a part, and has given it a place in a new context, the 
context and the place both being determinations made in inquiry, 
not native properties of original existence. Probably nowhere else 
is the work of judgment in discrimination and in creation of 
syntheses as marked as in historical evocations. Nowhere is it 
easier to find a more striking instance of the principle that new 
forms accrue to existential material when and because it is sub- 
jected to inquiry. 

What has been said finds its conspicuous exemplification in the 
familiar commonplace of the double sense attached to the word 
history. History is that which happened in the past and it is the 
intellectual reconstruction of these happenings at a subsequent 
time. The notion that historical inquiry simply reinstates the 
events that once happened "as they actually happened" is in- 
credibly naive. It is a valuable methodological canon when in- 
terpreted as a warning to avoid prejudice, to struggle for the 
greatest possible amount of objectivity and impartiality, and as an 
exhortation to exercise caution and scepticism in determining the 
authenticity of material proposed as potential data. Taken in any 
other sense, it is meaningless. For historical inquiry is an affair 
(1) of selection and arrangement, and (2) is controlled by the 
dominant problems and conceptions of the culture of the period 
in which it is written. It is certainly legitimate to say that a cer- 



NARRATION AND DESCRIPTION 237 

tain thing happened in a certain way at a certain time in the past, 
in case adequate data have been procured and critically handled. 
But the statement "It actually happened in this way" has its status 
and significance within the scope and perspective of historical 
writing. It does not determine the logical conditions of historical 
propositions, much less the identity of these propositions with 
events in their original occurrence. Das geschichtliche Geschehen, 
in the sense of original events in the existential occurrence, is called 
"geschichtlich" only proleptically; as that which is subject to se- 
lection and organization on the basis of existing problems and con- 
ceptions. 

A further important principle is that the writing of history is 
itself an historical event. It is something which happens and which 
in its occurrence has existential consequences. Just as the legends, 
monuments, and transmitted records of, say, Athens, modified the 
subsequent course of Athenian life, so historical inquiry and con- 
struction are agencies in enacted history. The acute nationalism 
of the present era, for example, cannot be accounted for without 
reckoning with historical writing. The Marxian conception of 
the part played in the past by forces of production in determining 
property relations and of the role of class struggles in social life has 
itself, through the activities it set up, accelerated the power of 
forces of production to determine future social relations, and has 
increased the significance of class struggles. The fact that history 
as inquiry which issues in reconstruction of the past, is itself a part 
of what happens historically, is an important factor in giving 
"history" a double meaning. Finally, it is in connection with 
historical propositions that the logical significance of the emphasis 
placed upon temporal continuity of past-present-future in dealing 
with the first two themes of this chapter most fully comes to light. 

Our entire discussion of historical determinations has disclosed 
the inadequacy and superficiality of the notion that since the past is 
its immediate and obvious object, therefore, the past is its exclusive 
and complete object. Books treat of the history of Israel, of 
Rome, of Medieval Europe, and so on and so on; of nations, in- 
stitutions, social arrangements that existed in the past. If we de- 
rive our logical idea of history from what is contained within the 
covers of these books, we reach the conclusion that history is 



238 THE STRUCTURE OF INQUIRY 

exclusively of the past. But the past is of logical necessity the past- 
of-the-present, and the present is the-past-of-a-future-living pres- 
ent. The idea of the continuity of history entails this conclusion 
necessarily. For, to repeat, changes become history, or acquire 
temporal significance, only when they are interpreted in terms of 
a direction from something to something. For the purposes of a 
particular inquiry, the to and from in question may be intelligently 
located at any chosen date and place. But it is evident that the 
limitation is relative to the purpose and problem of the inquiry; it 
is not inherent in the course of ongoing events. The present state 
of affairs is in some respect the present limit-to- which; but it is it- 
self a moving limit. As historical, it is becoming something which 
a future historian may take as a limit ab quo in a temporal con- 
tinuum. 

That which is now past was once a living present, just as the 
now living present is already in course of becoming the past of an- 
other present. There is no history except in terms of movement 
toward some outcome, something taken as an issue, whether it be 
the Rise and Fall of the Roman Empire, Negro Slavery in the 
United States, the Polish Question, the Industrial Revolution or 
Land Tenure. The selection of outcome, of what is taken as the 
close, determines the selection and organization of subject-matter, 
due critical control being exercised, of course, with respect to the 
authenticity of evidential data. But the selection of the end or 
outcome marks an interest and the interest reaches into the future. 
It is a sign that the issue is not closed; that the close in question is 
not existentially final. The urgency of the social problems which 
are now developing out of the forces of industrial production and 
distribution is the source of a new interest in history from the 
economic point of view. When current problems seem domi- 
nantly political, the political aspect of history is uppermost. A 
person who becomes deeply interested in climatic changes readily 
finds occasion to write history from the standpoint of the effect 
of great changes that have taken place over large areas in, say, the 
distribution of rainfall. 

There is accordingly, a double process. On the one hand, 
changes going on in the present, giving a new turn to social prob- 
lems, throw the significance of what happened in the past into a 



NARRATION AND DESCRIPTION 239 

new perspective. They set new issues from the standpoint of 
which to rewrite the story of the past. On the other hand, as 
judgment of the significance of past events is changed, we gain 
new instruments for estimating the force of present conditions as 
potentialities of the future. Intelligent understanding of past 
history is to some extent a lever for moving the present into a cer- 
tain kind of future. No historic present is a mere redistribution, 
by means of permutations and combinations, of the elements of 
the past. Men are engaged neither in mechanical transposition of 
the conditions they have inherited, nor yet in simply preparing for 
something to come after. They have their own problems to solve; 
their own adaptations to make. They face the future, but for the 
sake of the present, not of the future. In using what has come to 
them as an inheritance from the past they are compelled to modify 
it to meet their own needs, and this process creates a new present 
in which the process continues. History cannot escape its own 
process. It will, therefore, always be rewritten. As the new 
present arises, the past is the past of a different present. Judg- 
ment in which emphasis falls upon the historic or temporal phase 
of redetermination of unsettled situations is thus a culminating evi- 
dence that; judgment is not a bare enunciation of what already 
exists but is itself an existential requalification. That the requalifi- 
cations that are made from time to time are subject to the condi- 
tions that all authentic inquiry has to meet goes without saying. 

II. In what has been said attention has been given to the narra- 
tional propositions of existential judgment to the neglect of the 
descriptive. But things which happen take place in the literal 
sense of the word. The historian, as narrator, is primarily con- 
cerned with sequential occurrences with respect to their sequence. 
But he is quite aware that events do not occur just in time. They 
take place somewhere, and the conditions of this "somewhere" 
stand in coexistence with one another and also in coexistence with 
things taking place elsewhere. Locations, places, and sites are rela- 
tive to one another; they co-exist. Abstract time as a mathematical 
entity may be conceived as a unilinear dimension. But events do 
not occur in an abstraction; the historic line of sequence consists 
of many dimensions. If only one event occurred in, say, 1492, the 
year 1492 would not be a date in a historical calendar but a purely 



240 THE STRUCTURE OF INQUIRY 

mathematical conception, a pure number. It is not because of the 
sheer choice of historians nor because of literary quality and color 
that history cannot be written apart from geography, nor narra- 
tion proceed without description. 

Nor, on the other hand, has description significance apart from 
narration. In a biography, a portrait may be given by means of 
words or by a reproduction of a painting or a photograph. But the 
portrait is meaningless save in connection with a statement or esti- 
mate of the age of the person — whether explicitly given or in- 
ferred from the description, verbal or pictorial. A description 
consists always of coexisting characteristics that are so conjoined 
as to frame or outline an object or event in a way that affords the 
means for the identification of what is being described as the singu- 
lar existence which it is. The terms of the description are evi- 
dential marks. Whatever is the literary or esthetic office of 
description, its sole logical function is to enable identification to 
be made for the sake of determining the relevancy of this and that 
proposition. A man is said to answer to a certain description; it is 
found that a certain arrangement of coexisting finger-whorls is the 
most effective means of identification. To describe a geometrical 
figure is to traverse its outline not for an esthetic purpose but to 
set forth just that conjunction of traits which enables it to be 
surely identified. A scientific description is logically adequate 
in the degree in which it consists of a group of coexistent traits 
which so identify an object that anything having these traits, and 
only those having them, is of such and such a kind. To be of such 
and such a description is to be of such and such a kind. In the 
Aristotelian scheme of science, as we saw, the proper description 
was also ipso facto, the proper and final definition. In modern 
science, proper description is strictly a means of identification, 
while the particular identifications made are relative to the problem 
in hand. It may be physical, psychological, or moral, according to 
the identification needed in order to warrant special predica- 
tions. And any predication, as we have seen, is a requalification, 
or operational means of instituting a requalification, and so in- 
volves a change, which, when stated, is temporal-narrational. 

Descriptions are, then, existential propositions which are means 
to judgment but are not themselves final and complete — not judg- 



NARRATION AND DESCRIPTION 241 

merit itself. A single quality may serve as a diagnostic mark, as a 
certain quality of yellow in a flame is a sign of the presence of 
sodium. But a single trait is only the beginning of a description; 
it is an incomplete description. Thus "the man in the iron mask" 
is part of a description, but is not itself a description. It would 
be a description only if it were conjoined with other coexisting 
traits. The same thing is true of "the author of the letters of 
Junius"; "the man who invented the first wheel," and a multitude 
of other expressions. If the man in the iron mask should be 
identified (a complete description formed), then he would at once 
enter into a narrational sequence. When the partial description 
"the author of the Waverly Novels" was completed by uniting it 
with the characteristics of Sir Walter Scott, a large number of his- 
torical propositions about the author of the Waverly Novels at 
once became possible. If, however, "Sir Walter Scott" had no 
known characteristic except that of being the author of the 
Waverly Novels, there would be no coexistential conjunction, and 
we should be no better off than we were before. The sentence 
"Sir Walter Scott is the author of the Waverly Novels" is a com- 
plete proposition only because a number of other traits can be 
ascribed to him than that of being the author of the novels — a man 
born at a certain time, living in a certain place, having written 
poems, having a certain circle of friends, possessed of such and 
such qualities. From another point of view, the proposition links 
the life career of a certain man to the developing literature of the 
country — also a historical proposition. 

A conjunction of traits or a description is the basis of institu- 
tion of a kind, as will be shown in detail in the ensuing chapter. 
A proposition about a kind is general. Propositions which are 
linguistically expressed by proper names and by words like this, 
involve demonstrative reference to singulars. Hence it is often 
assumed in contemporary logical theory that there are such things 
as pure demonstrative propositions — "pure" in the sense that they 
involve no descriptive element. For example, in "That is a 
church," that would be called merely demonstrative, while in 
"That church is the Cathedral of St. John the Divine," that church 
would be called a mixed demonstrative descriptive term. While 
the notion of the logical difference between the two expressions 



242 THE STRUCTURE OF INQUIRY 

rests heavily upon a mere linguistic difference, it also goes back to 
a logical error which has been dealt with in other connections. 4 
It assumes that the subject-matter demonstratively present, which 
forms the logical subject, is immediately given. But determi- 
nation of a singular or this, requires selective discrimination. 
This discrimination must have a ground. The ground involves 
some conjunction of traits and hence provides at least a minimum 
of description. Only functional position in a contextual situation 
can discriminate an actual this from an indefinite number of po- 
tential thises. No one can tell what is pointed at in a given act of 
demonstration unless there is an idea of what is to be pointed out — 
that is, discriminatively selected. Mere pointing is completely in- 
determinate. 5 

Supposing it is asked "What is that?" That is certainly highly 
indeterminate. Otherwise there would not be the question as to 
'what it is. But there must be some minimum of descriptive de- 
termination involved, or otherwise neither the one asking the ques- 
tion nor the one of whom it is asked would know what the question 
was about. It might be any one of the great variety of objects 
that are in the general line of, say, the extended hand and index 
finger. In fact, that which is pointed to is that dark object or that 
suddenly moving thing, or is partially described, while the question 
shows that the descriptives dark or suddenly moving do not de- 
scribe sufficiently to determine its kind in connection with the 
problem in hand. It is an incomplete description for this reason. 
But the instance does not show that all identifying and demarcat- 
ing description is lacking, for such lack would be identical with 
complete absence of ground for further description. A person on 
a vessel at sea states, "There is a mountainous island." The person 
addressed replies, "No, it is a cloud." Unless there is some descrip- 
tive qualification that identifies what is meant by there and it, the 
two persons may be talking about entirely different objects. 
Common reference requires at least a minimum of description. 6 
Given that minimum, the difference between qualification as "is- 
land" and as "cloud" is a direct invitation to further observations 

4 See ante, p. 124 and p. 148. 
5 Cf. the illustration given on p. 53. 

6 As is exemplified in the ambiguity of reference of pronouns in a non- 
declensional language. 



NARRATION AND DESCRIPTION 243 

which will so analyze it as to discover, if possible, traits which 
justify one descriptive qualification or another. The theory criti- 
cized confuses an inadequate description of this (which is the basis 
for further operations of observation in order to ascertain the con- 
junction of traits upon which rests identification of it as one of a 
kind) with total lack of descriptive qualification. 

Propositions about a singular as one of a kind are dealt with 
later. At this juncture our discussion calls attention, in effect, to 
the double meaning of the words demonstration and proof. On 
the one hand, there is rational demonstration, an affair of rigor- 
ous sequence in discourse. On the other hand, there is ostensive 
demonstration. In the difference of opinion as to whether that is 
an island or a cloud, there is first an idea of the respective con- 
junctions of traits which describe the two kinds, and then there 
are the operations of observation which decide to which of the two 
descriptive prescriptions the object answers. If "this" does not 
turn out to be marked by traits which describe differentially the 
conceptions of mountains and islands, then it does not answer to 
that description. Were the theory of mere or pure demonstrative 
propositions sound, the failure to answer would have to be at- 
tributed to some property of the act of pointing — which is absurd. 
The important positive logical principle involved is that in all 
propositions of existential import, proof or demonstration is a mat- 
ter of the execution of delimiting analytic operations of observa- 
tion. Evidence not discourse is here what has probative force. 
The operations of observation executed are, however, controlled 
by conceptions or ideational considerations which define the con- 
ditions to be satisfied by differential traits in descriptive determina- 
tion of kinds. 

There is another mode of narrative-descriptive propositions the 
nature of which will be dealt with later. 7 Propositions that refer 
to courses of natural events are of this mode. The contents of 
physical laws and of the physical existences to which they refer 
are usually taken in logical theory to be non-historical. It is recog- 
nized, of course, that they are concerned with events that occur in 
time and in space. Although the conceptions of absolute time 
and space have been abandoned, the idea persists in logic that 

7 In Chapter XXII. 



244 THE STRUCTURE OF INQUIRY 

events in space-time can be regarded simply as specimen cases of 
laws. Because of this idea the determination of events is isolated 
in current logical formulation from the continuum of events with 
which they are constituents. This isolation is equivalent to ignor- 
ing the need for determining them as constituents of extensive 
historical events, in a sense in which "historical" has the same 
meaning that it has in determination of the course of human his- 
tories. The problem that is involved can be adequately discussed, 
however, only in connection with discussion of methods of scien- 
tific inquiry. Consequently, consideration of it is deferred until 
that topic is taken up. 



CHAPTER XIII 

THE CONTINUUM OF JUDGMENT: 
GENERAL PROPOSITIONS 



-^ xperience has temporal continuity. There is an experien- 
ced rial continuum of content or subject-matter and of opera- 
J^/ tions. The experiential continuum has definite biological 
basis. Organic structures, which are the physical conditions of 
experience, are enduring. Without, as well as with, conscious in- 
tent, they hold the different pulses of experience together so that 
the latter form a history in which every pulse looks to the past 
and affects the future. The structures, while enduring, are also 
subject to modification. Continuity is not bare repetition of identi- 
ties. For every activity leaves a "trace" or record of itself in the 
organs engaged. Thereby, nervous structures taking part in an 
activity are modified to some extent so that further experiences 
are conditioned by changed organic structure. Moreover, every 
overt activity changes, to some extent, the environing conditions 
which are the occasions and stimuli of further experiences. 

Hume, who carried the atomization of experiences to its ex- 
treme, was obliged on that account in order to obtain even a 
semblance of enduring objects, to introduce a counterbalancing 
principle, habit. Without this bond of connection neither memory 
nor expectation (to say nothing of inference and reasoning) could 
exist. Each new "impression" would be an isolated world of its 
own, without identifiable quality. He regarded habit as a "mys- 
terious tie" — but a tie he had to have in order to account for 
even the illusion of stable objects and of a self that endured 
through the succession of experiences. The development of bio- 
logical knowledge has now done away with the "mysterious" 
quality of the tie. Some sort of sequential connection is seen to be 

245 



246 THE STRUCTURE OF INQUIRY 

as inherent a quality of experience as are the distinctive pulses of 
experience that are bound together. Cultural conditions tend to 
multiply ties and to introduce new modes of tying experiences 
together. 

The process of inquiry reflects and embodies the experiential 
continuum which is established by both biological and cultural 
conditions. Every special inquiry is, as we have seen, a process of 
progressive and cumulative re-organization of antecedent condi- 
tions. There is no such thing as an instantaneous inquiry; and 
there is, in consequence, no such thing as a judgment (the conclu- 
sion of inquiry) which is isolated from what goes before and comes 
after. The meaning of this thesis is not to be confused with the 
trivial, because external, fact that it takes time to form a judgment. 
What is affirmed is that inquiry, which yields judgment, is itself a 
process of temporal transition effected in existential materials. 
Otherwise, there is no resolution of a situation but only a substitu- 
tion of one subjective unwarranted belief for another unwarranted 
one. 

While continuity of inquiry is involved in the institution of any 
single warranted judgment, the application of the principle extends 
to the sequence of judgments constituting the body of knowledge. 
In this extension, definite characteristic forms are involved. Every 
inquiry utilizes the conclusions or judgments of prior inquiries in 
the degree in which it arrives at a warranted conclusion. Proposi- 
tional formulations are the means of establishing conclusions. 
They consist of symbols of the contents that are derived from those 
phases and aspects of former inquiries that are taken to be relevant 
to the resolution of the given problematic situation. Scientific 
inquiry follows the same pattern as common sense inquiry in its 
utilization of facts and ideas (conceptual meanings) which are the 
products of earlier inquiries. It differs from common sense in the 
scrupulous care taken to ensure both that the earlier conclusions 
are fitted in advance to be means for regulation of later inquiries, 
and the care taken to ensure that the special facts and conceptions 
employed in the later ones are strictly relevant to the problem in 
hand. In common sense, the attitudes and habits formed in earlier 
experiences operate to a large extent in a causal way; but scientific 
inquiry is a deliberate endeavor to discover the grounds upon 



THE CONTINUUM OF JUDGMENT 247 

which attitudes and habits are entitled to operate causally in a 
given case. 

That earlier conclusions have the function of preparing the way 
for later inquiries and judgments, and that the later are dependent 
upon facts and conceptions instituted in earlier ones, are common- 
places in the intellectual development of individuals and the 
historic growth of any science. That continuity is involved in 
the maturing of individuals and the building up of the procedures 
and conclusions of bodies of knowledge is too obvious to demand 
argument. It would even be too obvious to be w^orth mentioning 
were it not that this continuity is something more than an in- 
dispensable condition of intellectual growth. It is the only prin- 
ciple by which certain fundamentally important logical forms 
can be understood; namely, those of standardized general concep- 
tions and of general propositions. The theme of the present 
chapter is then the connection between the continuum of inquiry 
and generality as a logical form. 

Singular events and objects are recognized, or in logical lan- 
guage, identified and discriminated, as such-and-such, or so-and-so. 
"Such" designates relation to something else to which a singular is 
likened in respect to quality, degree or extent, or to which it 
stands in some relation of dependence. Illustrations of the ex- 
plicit use of "such" in the first sense are found in such expressions 
as "such dire want"; "such soft music"; "such a hero"; "such 
opinions," etc. Examples of the second use are found wherever 
a comparison is made in which "as" (or so) and "such" are cor- 
relative: for example, "as is the teacher, so is the school," and other 
proverbial expressions, such as, "such the master, such the servant," 
while so as an equivalent of hence always indicates continuative 
logical force. 

All propositions regarding this or any singular, having the for- 
mal "is" as connective, express assimilation of this to other singulars 
in quality, degree or extent, as in "This is red," "This is rust," "This 
is oxide of iron," or "This is a noise," "It is a bang," "It is the back- 
firing of an automobile." The predicates, when formally gener- 
alized as descriptive terms, are represented as "such and such." 
The singular is described (discriminated and identified) as one of 
a kind by means of a conjunction of traits which make it like 



248 THE STRUCTURE OF INQUIRY 

certain other things already determined and that are likely to occur 
for determination in the future. These simple considerations are 
enough to establish a strong presumption of the connection be- 
tween the general and the principle of continuity, while the mean- 
ing to be ascribed to "likeness" constitutes a problem for further 
discussion. 

It is not uncommon to interpret the logical form under consid- 
eration by reference to a "common" factor which is instituted 
through recurrence. In some sense, this interpretation in terms 
of recurrence is justified since it marks recognition of some sort of 
continuity. But the problem is to ascertain the particular sense 
in which "recurrence" is to be taken. For when this conception 
is examined it is found to involve already the conception of kind, 
so that explanation of the conception of kind by that of recur- 
rence is simply a substitution of one word for another. For 
example, a given singular event is followed by the proposition 
"This is a flash of lightning." This flash is certainly not recur- 
rence in the sense of re-appearance of an object or event which has 
presented itself before and which has endured in existence during 
the interval. Clearly, recurrence here is practically synonymous 
with identification of the flash as one of a kind. We surely can- 
not, in this case, employ recurrence as something already under- 
stood by means of which to understand the conception of kind. 

At best, the explanation of kinds, which are general, on the basis 
of recurrence would apply only in the case of enduring objects 
which reappear in experience from time to time. We see the 
same mountain over and over again under a great variety of chang- 
ing circumstances. But this fact only guarantees the continuing 
existence of a singular. It leaves us without guidance or support 
in identifying another singular, not previously experienced, as a 
mountain, although it would support the inference that "// it is a 
mountain, it is enduring in temporal span." Recurrence is, in 
other words, one of the chief grounds for accepting belief in 
enduring objects which are not, like flashes of lightning, of very 
short duration. But it leaves the question of kinds just where it 
was. 

Moreover, the difference in question is at most but one of length 
of duration. A mountain lasts longer than a cloud, but we know 



THE CONTINUUM OF JUDGMENT 249 

that mountains had an origin and that they will, given a sufficiently 
long time, decay and pass out of existence. We also know that the 
span of a given object's duration is not determined by an inherent 
eternal essence, but is a function of the existential conditions which 
produce it and which sustain it for a few seconds, or minutes, or 
many thousands of years. In existential principle, there is no 
difference between the passing rain and the "everlasting" ocean. 
Propositions about the length of the duration of an object are 
matters of evidence, not of deduction from the concept of sub- 
stance. 

It is said that there are savage peoples who believe that the light- 
bringing object which sets at night is not the same object as that 
which rises and brings light the next morning. They are said to 
believe that there is a new sun every day. Whether the belief is 
actually held or not makes no difference for the purpose of illus- 
tration. For in any case, the experience is unique and non-recurrent. 
On what grounds do we draw a distinction between its unique 
character and the identity of the object which is its subject- 
matter? It will be a year before the sun presents itself again in 
the same position in the heavens, and perhaps it will never appear 
again under exactly the same conditions. The question is not 
meant to suggest any doubt about the enduring quality of the 
object in question. It is meant to indicate that the reasons for the 
belief are matters of fact, of evidence, which warrant a conclusion 
as an inference. 

Take the grounded proposition that the evening and the morn- 
ing star are the same planet. This is not an idea or a fact given 
in immediate experience. It is not an aboriginal datum within the 
experience. It is warranted in and by a highly complex set of 
observations as these are systematized by certain conceptions of 
the structure of the solar system. The case of the identity of 
the sun is simpler but it is of the same order. The only conclusion 
which can be drawn for logical theory from these considerations 
is that the problem of the sameness of the singular object is of the 
same logical nature as the problem of kinds. Both are products of 
the continuity of experiential inquiry. Both involve mediating 
comparisons yielding exclusions and agreements and neither is a 
truth or datum given antecedent to inquiry. 



250 THE STRUCTURE OF INQUIRY 

They are not only products of the same operations of inquiry 
but are bound up together. The determination that a singular is 
an enduring object is all one with the determination that it is one 
of a kind. The identification of a sudden light as a flash of light- 
ning, of a noise as the banging of a door, is not grounded upon 
existential qualities which immediately present themselves, but 
upon the qualities with respect to the evidential function or use 
in inquiry they subserve. What is recurrent, uniform, "common," 
is the power of immediate qualities to be signs. Immediate quali- 
ties in their immediacy are, as we have seen, unique, non-recurrent. 
But in spite of their existential uniqueness, they are capable, in the 
continuum of inquiry, of becoming distinguishing characteristics 
which mark off (circumscribe) and identify a kind of objects or 
events. As far as qualities are identical in their functional force, 
as means of identification and demarcation of kinds, objects are 
of the same kind no matter how unlike their immediate qualities. 
Scientific kinds are determined, for example, with extreme dis- 
regard of immediate sensible qualities. The latter are irrelevant 
and often obstructive in the institution of extensive systems of 
inference and hence are not employed to describe kinds. 

A singular as a mere this, always sets a problem. The problem 
is resolved by ascertaining ivhat it is — that is, the kind it is of. 
This fact alone is enough to show the identity of the two appar- 
ently different matters of determining the temporal endurance of 
an event and determining its kind. "This" is an intellectual puzzle 
until it is capable of being described in terms of what, linguisti- 
cally, is a common noun. The description is qualification of the 
singular as one of a kind. The question, then, concerns the way 
in which the general form is instituted, it being noted that recur- 
rence is connected with inference and not with existences apart 
from their function in inference. 

A starting point for further discussion is found in the fact that 
verbal expressions which designate activities are not marked by the 
distinction between "singular" (proper) names and "common" 
names, which is required in the case of nouns. For what is des- 
ignated by a verb is a "way of changing and/or acting. A way, 
manner, mode, of change and activity is constant or uniform. It 
persists, although the singular deed done or the change taking 



THE CONTINUUM OF JUDGMENT 251 

place is unique. An act and a change can be demonstratively 
pointed out, and qualified as one of a kind, for example, a foot- 
race or a fire. But racing and burning are 'ways of acting and 
changing. They are exemplified in singulars but are not them- 
selves singular. They may recur; they represent possibilities of 
recurrence. A way of operating employed to characterize a 
singular gives the latter potential generality. When the potential 
activity of, say, walking, is actualized, there comes into existence 
a walk. When the process of burning is actualized in a singular 
there is a fire. It is still a singular or this but it is a singular of a 
kind. 

Because of the operation of tasting and touching, this is affirmed 
to be sweet and hard. The operation, being a constant, recurs. 
Its consequence may be that the particular this of a new experi- 
ence is affirmed to be sour and soft. Discrimination occurs because 
of consequences of agreement and difference — because agreements 
and exclusions are instituted by recurring operations in the experi- 
ential continuum. The outcome is that the presence of certain im- 
mediate qualities is so conjoined with certain other non-immediate 
qualities that the latter may be inferred. When this further opera- 
tion of inference takes place, the potential generality, due to the 
presence of the same modes of change and activity, is actualized. 
The resulting inference is grounded in the degree to which differ- 
ential consequences are instituted so that some conjoined traits 
are inferable while other traits are excluded. 

The connection of inference with expectation was correctly 
pointed out by Hume. He obtained a merely sceptical conclusion 
from this connection because (1) he never pursued his analysis 
of the "mysterious" principle of habit to the point of seeing its 
identity with a uniform mode of operation and change, and be- 
cause (2) he failed to note that explicit formulation of an ex- 
pectation renders it capable of being checked and tested by 
consequences, positive and agreeing, negative and excluding, while 
(3) such formulation transfers expectation from the field of 
existential causation to the logical realm. A generality is involved 
in every expectation as a case of a habit that institutes readiness 
to act (operate) in a specified way. This involvement yields 
what was called potential logical generality. Explicit formulation 



252 THE STRUCTURE OF INQUIRY 

in prepositional form of the expectation, together with active use 
of the formulation as a means of controlling and checking further 
operations in the continuum of inquiry, confers upon the poten- 
tiality a definite logical form. 

The burnt child dreads the fire— an expectation and a potential 
generalization on the part of the child. The Egyptians looked 
forward to the occurrence of eclipses at specified dates. In so 
far as past occurrences had been analyzed sufficiently to furnish 
the ground for the expectation, the latter partook of the nature of 
inference. In as far, however, as merely temporal occurrences 
were the ground of the prediction, the latter was not inference in 
its definitive logical sense. It became such inference when certain 
constant modes of natural operation were ascertained to be the 
reason why certain conjunctions of circumstantial conditions 
could be used to ground a prediction. 1 

We are brought to the conclusion that it is modes of active 
response which are the ground of generality of logical form, not 
the existential immediate qualities of that which is responded to. 
Qualities which are extremely unlike one another in their imme- 
diate (or "sensible") occurrence, are assimilated to one another 
(or are assigned to the same kind) when the same mode of response 
is found to yield like consequences; that is, consequences subject 
to application of one and the same further operation. A flash of 
lightning is very different in its sensible setting from the electric 
spark which had been observed before the time of Franklin, as 
well as from the attraction exercised by amber when rubbed, as 
also from the tingling sensation experienced when under certain 
atmospheric conditions a person who has scuffed his feet touches 
another person. The assimilation of such phenomena and a great 
many others to one another, as of the kind electro-magnetic, did 
not come about by searching for and finding "common" imme- 
diate qualities. It was effected by employing modes of operation 
and noting their consequences. Similarly, the generalization of 
the three states of matter, solid, liquid and gaseous, was obtained 
by operations of experimental variation of temperature and pres- 

1 In the sense in which "empirical" is distinguished from "rational" on the 
ground of likeness of existential conditions, "empirical" inference is a mixture of 
expectations causally produced and inference in its logical sense. 



THE CONTINUUM OF JUDGMENT 253 

sure and noting their consequences. Until this was done, certain 
things like air, seemed to be inherently or by their "essence" a 
gas. One has only to note the way in which scientific kinds are 
formed to be convinced that assimilation of different objects and 
events into kinds is not constituted by comparison of immediately 
given qualities along with "extraction" of those which are "com- 
mon" but by the performance of operations which determine the 
presence of modes of interactions having specified consequences. 
"Common" designates, not qualities, but modes of operation. 2 

As has already been noticed, such expressions as "This is red, 
liquid, soluble, hard" are not primary, but express the consequences f 
actual or anticipated, of execution of operations. As qualifications, 
or as actual and possible predications, they are effected by the 
cumulative force of the recurrence of operations, similar and dif- 
ferentiating. The cumulative force of these observations issues 
in such propositions as "This is sugar," "That is a race horse," etc. 
In these propositions, the predicates represent potentialities which 
will be actualized when certain further operations are performed 
that produce interactions by introduction of new conditions. An 
actual, immediate quality thus becomes a sign of other qualities 
that will (or would) be actual if additional operations producing 
conditions for new modes of interaction w T ere performed. When 
it is said, for example, "This is iron," the significance of the qualifi- 
cation iron consists of potentialities not then and there actualized. 
The qualities of "this" are actual. But they are taken not in their 
bare actuality but as evidential signs of consequences that will be 
actualized when further interactions are instituted. The impor- 
tance of scrupulous determination, by observation, of existing 
qualities, is instrumental; it is a matter of instituting data for a 
controlled and grounded inference. Fulfilment of this condition 
demands, logically, variation of the operations of observation. The 
immediate qualities of iron pyrites suggest the proposition "This 
is gold." If the suggestion is immediately acted upon, the one 
who drew that conclusion finds himself, after a waste of time and 
energy, to be deluded. Care is taken in scientific inquiry, as 
distinct from the formation of common sense expectations, to 

2 Compare what was said earlier about exclusion and negative as active processes, 
See pp. 181 seq. 



254 THE STRUCTURE OF INQUIRY 

determine in advance whether given qualities are such as to be 
the differential traits which describe the thing as of a specified 

kind. 3 

The discussion has so far been occupied with generals in the 
form of a set of conjoined traits describing a kind. It has been 
shown that qualities become traits descriptive of a kind when they 
are the consequences of operations which are modes or ways of 
changing and acting. This fact indicates that the operations are 
themselves general, although in another sense from the generality 
attached to sets of conjoined traits. It indicates, indeed, that the 
type of generality which constitutes the logical form of the latter 
is derivative, depending upon the generality of the operations 
executed or possible. The discussion has thus arrived at a point 
where it is necessary to discriminate between two types or logical 
forms of generality. Historically, the generality of kinds came 
first. For men are customarily more concerned with the conse- 
quences, the "ends" or fruits of activity, than with the operations 
by means of which they are instituted. The direct result of this 
historical fact in logical theory was the conception of natural 
kinds or species (or "classes") and the construction of classificatory 
and taxonomic science. Even after the logical priority of opera- 
tions in determination of kinds had become a commonplace of 
scientific practice, the priority and prestige of the conception of 
"classes" operated in logical theory to obscure recognition of the 
form of generality which is logically prior and conditioning. In- 
deed, it has done more than obscure it. It has resulted in the 
widespread confusion found in the attempt to interpret all logical 
generals on the ground of a theory of classes. Accordingly, not 
only the intrinsic merits of the case, but a prevalent confusion in 
logical theory, demands that special attention be given to the 
distinction and the relation of the two forms of generality. 

The conclusion of the discussion of this point will be antici- 
pated by the use of certain words to mark the distinction. Propo- 
sitions about kinds and classes in the sense of kinds will be called 

3 The proposition "This is iron pyrites" is not in such a case itself an inference 
but an expectation. For the proposition is determined directly and sufficiently 
only by operations of experimental analysis which determine qualities as traits 
descriptive of a definitive kind. This point has important bearings upon the theory 
of induction, as is pointed out later. (See Chap. XXI) 



THE CONTINUUM OF JUDGMENT 255 

generic propositions (in the sense in which species are also, as 
kinds, generic), while propositions whose subject-matter is pro- 
vided by the operation by means of which a set of traits is 
determined to describe a kind, will be called universal. Corre- 
spondingly, the universals as such, will be called categories, in order 
to avoid the ambiguity found in the current use of the term 
"classes" in logical theory — the word "class" being used to desig- 
nate both kinds and universals, which in logical function and 
form are distinct, as is shown later. 

There are words in common use whose meaning is systemati- 
cally ambiguous, for instance such words as "if, when, conditions." 
Sometimes they refer to the existential and sometimes to the idea- 
tional. When it is said, "If he doesn't come in five minutes I 
shan't wait any longer" — "if" refers to a set of contingent temporal- 
spatial circumstances. Similarly, when it is asked, "When does 
the sun rise tomorrow?" the reference is clearly to an occurrence 
in time. But the word "when" in the clause u <when it is asked" 
has quite a different force. It means "whenever," or if at any 
time such a question should be asked, without implying that it 
has been asked or will, as a fact, ever be asked. The proposition 
"When angels appear, men are dumb" does not of itself imply 
that angels exist or will ever appear. In science, there are many 
propositions in which the clause introduced by "if" is known to 
be contrary to conditions set by existential circumstances; that is, 
to be such that they cannot be existentially satisfied, as "If a 
particle at rest is acted upon by a single moving particle, then," 
etc. In such propositions, if and when designate a connection of 
conceptual subject-matters, not of existential or temporo-spatial 
subject-matters. If the word "conditions" is used, it now refers to 
a logical relation, not to existential circumstances. 

In certain contexts, the distinction is recognized in present logi- 
cal theory: for example, in the doctrine that an A or E proposition 
does not imply an / or O proposition, and in the distinction made 
between mathematical and physical propositions. These considera- 
tions alone indicate the necessity of systematic recognition of two 
distinct logical forms of generality. The failure to carry the dis- 
tinction through in a systematic way appears to be due to an at- 
tempt to reduce general propositions about kinds (under the name 



256 THE STRUCTURE OF INQUIRY 

of classes) to the form of abstract universal propositions. The 
ultimate source of this attempt appears in turn to have its source 
in the fact that in the Aristotelian logic, kinds, as species, were 
interpreted as ontological universals. The development of modern 
logic, especially under the influence of mathematical science, has 
shown that universal propositions are abstract hypothetical propo- 
sitions, or non-existential in import. Hence confusion arises in 
logical theory when propositions about kinds (general in the sense 
of generic) are identified with universal propositions. 

Every modern text on logic points out the ambiguity in such 
propositions as "All men are mortal." In one interpretation, that 
sanctioned by tradition, it means that the class of men (in the 
sense of kind), is included within the class of mortal things. 
Stated explicitly in its existential import it means "All men have 
died or will die" — a spatio-temporal proposition. On the other 
hand, it means that "If any thing is human, then it is mortal": a 
necessary interrelation of the characters of being human and being 
mortal. Such a proposition does not imply nor postulate that 
either men or creatures who die actually exist. It would be valid, 
if valid at all, even if no men existed, since it expresses a necessary 
relation of abstract characters. On the other hand, the proposition 
"All men are mortal" interpreted in its existential reference is 
logically an / proposition, and being of the inductive order is 
subject to the contingencies of existence and of matter-of-fact 
knowledge. It is a proposition of a certain order of probability. 
The connection between the fact of life and the -fact of death is of 
a different logical form from the relation between being human 
and being mortal. The latter is valid, as just stated, if valid at all, 
by definition of a conception. The former is a matter of evi- 
dence, determined by observations. 

So far there is relatively clear sailing. But the distinction is 
often followed in contemporary logical texts by the assumption, 
explicit or implicit, that propositions about kinds are ultimately 
of the same logical dimension as are if-then universal propositions. 
The reasoning that leads to this assumption — or conclusion — is as 
follows. Propositions about kinds are not about the individuals 
of the kind, but about a relation of characteristic traits which de- 
termine the kind. The affirmation that "All individuals of the 



THE CONTINUUM OF JUDGMENT 257 

kind men are included in the more extensive kind mortals" does 
not involve acquaintance with all individuals, or even with a 
specified person. It applies to men not yet born as well as to an 
indefinite multitude of others with whom we have no acquaint- 
ance. Such propositions are therefore different in logical form 
from any proposition about a singular. 

The proposition "Socrates is a man" is, for example, of a differ- 
ent logical form from the proposition "All Athenians are Greeks." 
The former is restricted to a singular who must, in order to warrant 
the proposition, be capable of demonstrative reference. The latter 
by its nature goes beyond singulars capable of being demonstra- 
tively referred to — this is the essence of its generality. The rela- 
tion between the traits or distinguishing characteristics which 
determine the kind, men or Athenians, and the distinguishing 
characteristics which determine the kind, mortals or Greeks, is 
affirmed independently of demonstrative reference to any particu- 
lar given singular. Hence it is frequently said to be affirmed 
independently of reference to singulars as such. It is assimilated in 
form to the abstract non-existential universal proposition. 

The fallacy of the argument resides in identification of absence 
of reference to specified individuals or singulars with absence of 
reference to singulars as such. There is a clear difference between 
a proposition that refers to each and every individual who 
has certain characteristics (whether or not all individuals are 
known who have such characteristics), and a proposition 
that refers in its own content to no individual. It is true 
that the former is directly about a conjunction of characteristics 
and not about singulars as such. But it is equally true that it 
is about a set of characteristics that so describes a kind as to have 
reference to all (each and every) singular existences having the 
set of traits in question. "Each and every whale, whether ob- 
served or not, or whether now existent or not, is a mammal." "If 
an animal is cetacean, it is mammalian." When we compare these 
two propositions as to their logical form, it is evident that the latter 
expresses a necessary relation of characters and holds whether 
whales exist or not. The first proposition refers to each and every 
existence marked by a certain conjunction of traits. Independence 
of reference to that which exists at a particular time or place can- 



258 THE STRUCTURE OF INQUIRY 

not be identified, save by radical confusion, with the absence of 
reference to spatial-temporal circumstances as such, the latter being 
inherent in the universal proposition. 

The confusion is fostered by the logically ambiguous character 
of language— as in the double sense of "all" already mentioned. 
Linguistically, propositions about kinds are expressed by common 
nouns, and hypothetical universal propositions by means of abstract 
nouns; both of them being distinguished, of course, from proper 
nouns and from demonstratives like "this" and "here." But in 
many cases words in use fail to indicate by their linguistic form 
of which category they are. "Mankind," for example, designates 
explicitly a kind; "Humanity" may be an equivalent common 
noun or it may designate a relation of universal characters: the 
quality or state of being genuinely human. An even better ex- 
ample is "color." When it is said that red, green, blue, etc., are 
colors, the reference is clearly to kinds included in a more generic 
kind. But there is no abstract noun "colority" in common use. 
When Mill says that when it is affirmed "Snow is white, milk is 
white, linen is white, we do not mean that these things are 2. color 
but that they have a color," he speaks, of course, correctly. But 
then he proceeds to state "Whiteness is the name of the color 
exclusively." 4 Now a statement like Mill's implies that the dif- 
ference between having a color and being colority is simply that 
between a quality referred to a thing as its property and the same 
quality taken without reference to a thing. But whiteness does 
not designate a color as a quality at all. It designates a certain 
way or mode of being colority, the abstract universal. A white 
thing may suggest whiteness, but whiteness is not a color which 
things have or can have. We may dwell upon a given quality of 
color without reference to other qualities indefinitely in isolation. 
But it still remains a quality, white, not whiteness. The scientific 
conception of colority is of a different logical dimension from 
that of colors and a color. Colority or being color is defined in 
terms of rates of vibration and whiteness is defined as the functional 
correlation of the radiating-absorptive capacity of these vibrations 
combined in a stated proportion. It is in effect a definition of 

4 Mill, Logic. Book I, Ch. 2, Sec. 4. 



THE CONTINUUM OF JUDGMENT 259 

conditions to be satisfied if a proposition, "This is white," is war- 
ranted. 

Mill goes on to raise the question whether abstract words like 
whiteness are general or singular. Perplexed by certain considera- 
tions which will be presently noticed, he concludes that "the best 
course would probably be to consider these names as neither 
general nor individual, and to place them in a class apart." The 
conclusion does Mill's sense for logical forms credit: the "class 
apart" is, in fact, that of abstract universal. When he says they 
are not "general," he is using the word in the sense in which 
common nouns like color are general. His perplexity was then 
due to a belief that some abstract terms are names of an exten- 
sive kind. Color, for example, includes, according to him, white- 
ness, redness, blueness, etc.; and whiteness, in turn, includes 
various degrees. The same thing holds, he says, of magnitude and 
weight with reference to their various degrees. But such terms 
as equality, squareness, etc., designate, he says, an attribute "that 
is one and does not admit of plurality." Curiously enough he in- 
cludes "visibility" in the same category — although it is evident 
that it does have degrees. 

It is evident, I think, that Mill, when he speaks of abstract terms 
which, like common nouns, have extension of kinds or degrees, 
has slipped over from the abstract to existential objects and then- 
qualities. Objects do have various sizes or degrees of magnitude 
and various weights. It is impossible to see how the abstract con- 
ception of magnitude or heaviness can have degrees any more than 
can squareness or equality. Since different objects may be equal 
to one another in magnitude, while they differ in size from 
some other objects, his reasoning in the case of magnitude would 
logically lead to the conclusion that equality is also a name "for 
a class of attributes," since objects have different sizes and yet 
some are nevertheless equal to others. With respect to magnitude, 
a big object exemplifies it in no other way than a small one; with 
respect to exemplification of weight in the abstract there is no 
difference between a heavy object and a light one. Redness, blue- 
ness, whiteness, are ways of being colority, not kinds of color (in 
the concrete), like red, blue and white. 

The reference to Mill will be misunderstood if taken to apply 



260 THE STRUCTURE OF INQUIRY 

to him peculiarly among writers on logic. He simply makes ex- 
plicit a confusion that is implicit in many writers on logical theory. 
Exactly the same confusion exists when propositions like "All 
whales are mammals" are equated in logical form to propositions 
like "All squares are rectangular." For the latter proposition is 
not one about inclusion of kinds, but about a mode or way of 
being rectangular. 5 

I close this phase of the discussion by mentioning some distinc- 
tions of terminology which will be instituted and observed in 
order that there may be a suitable measure of linguistic protection 
against the confusion which has been described. As already stated, 
general propositions about kinds, or generals having existential 
reference, will be called generic propositions and terms. General 
propositions of the abstract if-then form will be called universal 
propositions. The word class is now used to designate both kinds 
and the different ways of being universal; for example, triangle 
is said to be a class including right-angled, scalene and isosceles 
triangles, thus making it much easier to confuse the logical form 
appropriate to kinds with the logical form appropriate to mathe- 
matical subject-matter. I propose to use the word class, when it 
is employed, as an equivalent of kind, and to use the word category 
for the other logical meaning. Triangularity, for example, is a 
category of which various ways of being triangular are sub- 
categories. Qualities which descriptively determine (distinguish 
and identify) kinds, I shall indifferently call traits or characteris- 
tics, while the related contents of an abstract universal proposition 
are called characters* 

More will be said later about the ambiguity of the conception 
of "inclusion." When kinds are affirmed to be included in a kind 

5 The verbal ambiguity already mentioned is found in the word "square" when 
used mathematically. It looks like a concrete word, while in fact it means square- 
ness, so that the proposition that reflects its logical meaning would be expressed 
in verbal form "Squareness is a mode of rectangularity." Similarly, "circle" in its 
mathematical use means circularity; its analytic expression in an equation obviously 
has no direct reference to objects or to qualities. The connection of the point 
here under discussion with the conception of operations developed in the first 
section of this chapter is taken up in the next chapter. 

6 Mill set the example of using the term "attributes" so loosely as to apply to 
qualities in the concrete, to traits and to what are here called characters. If the 
word "attributes" is used at all, it would be better, I think, to use it as a synonym 
for "characters." 



THE CONTINUUM OF JUDGMENT 261 

of wider extension, the reference of "included" is clearly existen- 
tial. But when a definition of polygon in geometry is said to 
"include" that of triangles, rectangles, etc., the meaning is very 
different. The Oxford Dictionary has a quotation which may be 
used to illustrate this type of meaning. "It is necessary to include 
in the idea of Labour all feelings of a disagreeable kind . . . con- 
nected with the employment of one's thought or muscles or both 
in a particular occupation." 

"Inclusion" is here connected with definition of an idea or 
conception. The quotation is saying that any definition of labor 
(here employed as an abstract word) is defective which does not 
contain as an integral or necessary part of its conception the idea 
of disagreeableness. If, or when, the definition is accepted, it af- 
fords a necessary logical condition of determination whether a 
given occupation is of a kind to be included (in the other sense of 
inclusion) in the kind of occupations that are laborious. Ac- 
cording to the definition, a proposition that such and such an 
occupation is or is not labor will depend for its differentia upon 
the presence or absence of a disagreeable quality attending its 
pursuit. A different definition or conception of labor might yield 
a different set of traits by which to assign an activity to a kind 
and to determine the relation of kinds. The instance illustrates 
the necessary relation subsisting between determination of generic 
propositions and the universal abstract propositions which are 
definitions of conceptual or ideational meanings. But it also in- 
volves their difference with respect to logical form, covering also 
the formal difference in the conceptions of inclusion and exclusion. 
A rule for inclusion and exclusion is not itself a case of the in- 
clusions or exclusions which its application effects. To preclude 
or rule out by definition is a different logical matter from refusing 
on evidential grounds to place one kind within another kind. 

In the next chapter, we shall return to a detailed consideration 
of generic and universal propositions in the light of the distinction 
of logical forms which has been formulated. In the state in which 
logical theory now exists, it is necessary, however, to engage in 
a discussion which would be an irrelevant excursus if the distinc- 
tion were acknowledged and systematically adhered to. The pres- 
ent phase of the discussion may be concluded by saying that three 



262 THE STRUCTURE OF INQUIRY 



logical motifs seem to have converged to bring about failure to 
recognize the distinction of logical forms. One of them is the 
influence of the Aristotelian identification of classes, as fixed on- 
tological species defined by a formal essence, with the universal. 
The second is the desire to maintain the strictly formalistic con- 
ception of logic (ruling out of all existential and material refer- 
ences) by setting up mathematical propositions as the logical form 
normative for the interpretation of the form of all general propo- 
sitions — a conception, however, which if it were rigorously main- 
tained would demand elimination of all demonstrative reference 
and hence, ultimately, of singular and generic propositions. The 
third influence springs from a consideration inherent in inquiry 
itself, namely, the necessary function of universal propositions in 
determination of warranted singular and generic propositions, a 
point discussed at length in the ensuing chapter. 

The problem of the nature of the general has been such a 
crucial issue in the history of both philosophic logic and meta- 
physical theory that a few words are added to indicate the traits 
which differentiate the position taken in this chapter from the 
views traditionally known as realism, conceptualism and nominal- 
ism—to differentiate it rather than here to argue for it and against 
the other interpretations. The theory agrees with the "realistic" 
interpretation of generals in affirming that ways of acting are as 
existential as are singular events and objects. It disagrees in that 
it holds that while these ways of interaction are necessary condi- 
tions, they are not sufficient conditions of logical generality, since 
the latter accrues only when and as the existentially general is used 
as a controlling function, in the continuity of inquiry, to attain 
warranted assertibility. 

In consequence, the theory agrees with "nominalism" in holding 
not only that immediate qualities are the ground required for 
determination of a specified generality which is possessed of ex- 
istential reference and also for test of its applicability in a given 
case, but (what is here more important) that the logically general, 
whether generic or universal, has necessarily the character of a 
symbol. For since it is not a literal transcription of a general in 
existence but is a utilization of the latter for the special purpose 
of inquiry (being, that is, a distinctively logical form), the status 



THE CONTINUUM OF JUDGMENT 263 

and function of a symbol is that of a required member of a propo- 
sitional form, while propositional formulation is inherently neces- 
sary for controlled inquiry. It differs fundamentally from 
nominalism in holding not only that the general has its ground in 
existence (and hence is not a mere convenient memorandum or 
notation for a number of singulars), but that symbolization is a 
necessary condition of all inquiry and of all knowledge, instead of 
being a linguistic expression of something already known which 
needs symbols only for the purposes of convenient recall and 
communication. 

Consequently, it agrees with "conceptualism" in the one point 
that the general is conceptual or ideational in nature. But it differs 
radically in its conception of what conceptions intrinsically are. 
Negatively, as has already been pointed out, it rejects completely 
the view that a conception represents simply a selection of material 
that is found to be antecedently "common" to a number of singu- 
lars. This rejection depends (1) upon interpreting the "common" 
in terms of the function performed by existential qualities in in- 
ference, and (2) upon the necessity of the abstract universal in 
order to warrant inferential use of qualities in any inquiry. The 
latter consideration is the more important in that it indicates the 
logical necessity of conceptions which, while they are suggested 
by singulars, are not logically derived from them, even from that 
which is common among them. For an idea or conception is the 
nature of a possibility and hence is of a different dimension from 
actuality, no matter how frequently repeated or "common" the 
actual quality may be. This conceptual dimension is, further- 
more, held to be logically an objective necessary condition in all 
determination of warranted beliefs or knowledge, not a psycho- 
logical accretion — as seems to be implied in traditional conceptual- 
ism. 



CHAPTER XIV 

GENERIC AND UNIVERSAL PROPOSITIONS 



I. Introduction. There are two forms of general propositions, 
the generic and the universal. Universal propositions are formu- 
lations of possible ways or modes of acting or operating. Proposi- 
tional formulation is required for control of a way of acting that 
effects discrimination and ordering of existential material in its 
function as evidential data. Execution of the operation that is 
prescribed and directed by the universal proposition in serving 
this function also tests the force and relevancy of the universal 
proposition as a means of solution of the problem undergoing 
resolution. For the universal is stated as a relation of an antecedent 
if content and a consequent then clause. When its operational 
application determines existential conditions which agree with the 
contents of the then clause, the hypothesis is in so far confirmed. 
But its affirmation is not sufficiently warranted; agreement is a 
necessary but not sufficient test. For an affirmation of the ante- 
cedent merely because the consequent is afflrmable is fallacious. 
Eliminations or negations have to be affected which determine 
that only if the antecedent is affirmed does the consequent follow. 

Application to existential material of the operation that is for- 
mulated in the universal proposition determines the material in 
question to be of specified kinds, and, by means of conjoint execu- 
tion of operations of inclusion-exclusion, determines the kinds to 
be the included members of an inclusive kind, and the only in- 
cluded kinds as far as the logical conditions of inclusion and 
exclusion are completely satisfied — a satisfaction which in fact can 
never be completely achieved because of the contingent nature of 
existential material, although the required satisfaction is approxi- 
mated in the continuity of inquiry as a long run procedure. 

There are organic activities upon the biological level which 

264 



GENERIC AND UNIVERSAL PROPOSITIONS 265 

select and order existential conditions in a & facto way. If a 
lower organism were equipped with powers of symbolization the 
result would be its ability to refer some things to certain gross 
generalizations or kinds — to sort them out, for example, as foods, 
as inedibles, and as poisons; and into things harmful and adverse 
and things helpful and favorable — foes and friends. The cultural 
matrix not only supplies, through the medium of language, means 
for explicit formulation of kinds but also extends vastly the 
variety and number of kinds. For culture institutes and consists 
of a vast number of ways of dealing with things. Moreover, 
certain ways of action are formulated as standard and normative 
rules of action and of judgment on the part of members of the 
cultural group. As was shown earlier, common sense consists, in 
its generalized phase, of a body of such standardized conceptions 
which are regulative (or are rules) of the actions and beliefs of 
persons as to what is proper and improper, required, permitted and 
forbidden in respect to the objects of the physical and social 
environment. Thus things and persons are sorted out into dis- 
tinctive kinds on the ground of allowable and prohibited modes 
of acting toward and with them: a practical foreshadowing of 
operations of inclusion and exclusion in the logical sense. 

But there is only a foreshadowing. For human beings are "nat- 
urally" interested in consequences, outcomes and fruits, good and 
bad, rather than in the conditions, material and procedural, by 
which they are obtained. Moreover, the standardized conceptions 
and rules are for the most part products of habit and tradition. 
Hence they are so fixed that they are not themselves open to 
question or criticism. They operate practically to determine kinds 
but the grounds or reasons for the kinds that are acknowledged in 
practice are not investigated or weighed — it is enough that the 
customary rules are what they are. From the logical standpoint, 
there is a vicious circle. Fixed, unquestioned rules determine the 
recognized kinds, while kinds are so fixed by the rules that 
they do not serve to test and modify the ruling conceptions but 
are taken rather to exemplify and support the rules. At best, 
inquiry is confined to determining whether or not given objects 
have the traits that bring them under the scope of a given stand- 



266 THE STRUCTURE OF INQUIRY 

ardized conception— as still happens to a large extent in popular 
"judgments" in morals and politics. 

The process of inquiry as inquiry consists, accordingly, of treat- 
ing the general propositions that are formulations of ways of 
action as hypotheses— a mode of treatment that is equivalent to 
treating the formulated modes of action as possible, instead of as 
required or necessary. This way of treating conceptions has its 
direct impact also upon formation of kinds. For it demands that 
grounds for them be searched for, and the grounds must be such 
as to satisfy (inclusively and exclusively) the requirements of the 
hypothesis that has been adopted and employed. Since existence 
is existence and facts about it are stubborn, ascertained facts serve 
to test the hypothesis employed; so that when there is recurrent 
discrepancy of observed facts with the requirements of the con- 
ception (hypothesis or theory), the material ground is provided 
for modification of the hypothesis. Here also is a circular move- 
ment, but it is a movement within inquiry, controlled by the 
operations by means of which problematic situations are resolved. 

II. Inference from Case to Case. It is convenient to begin the 
discussion by reference to the view of Mill, since he holds that 
generalizations proceed from singulars to other singulars and are 
proved by a sufficient number of particular cases, while he also 
admits that a "generalizing propensity" is involved when we pro- 
ceed from one observed singular to others that are unobserved. 
"We conclude," he says, "from known to unknown cases by the 
impulse of the generalizing propensity." 1 The generalizing im- 
pulsive propensity may be fairly identified with the mode of action, 
organic or acquired, of which mention has been made. But in 
Mill's account of generalization, the need for propositional for- 
mulation of the active propensity is not recognized. Consequently, 
his account of the production and nature of general propositions 
sets forth, quite precisely, what happens in the case of those gen- 
eralizations which fail to satisfy logical conditions: the generaliza- 
tions (of which mention was made in the introductory paragraphs) 
that do not rest upon ascertained grounds and which, therefore, 
are unwarranted. 

His well-known illustration of the village matron and her 

1 Logic, Book I, ch. 3, sec. 8. 



GENERIC AND UNIVERSAL PROPOSITIONS 267 

neighbor's child affords, when it is analyzed, proof of this state- 
ment. The matron infers from case to case by virtue of a gen- 
eralizing propensity. Since this remedy cured my child, it will 
cure yours. No doubt there are many cases in which just this 
procedure is followed. If it were not, patent medicine testimonials 
would not have the vogue they have. But the fact that the pro- 
pensity operates simply as a propensity and not through the me- 
dium of a general proposition of the if-then form (and hence 
checked by the consequences that ensue from its operation) is 
precisely the reason for the relative worthlessness of the inferences 
which result. The propensity is a cause of the inferences that are 
made but is no sense their ground. 

There is (1) no reason or ground for the village matron's as- 
sumption that it was the medicine recommended that in fact cured 
her own child. There is (2) no reason for the assumption that 
the disease of the neighbor's child is similar to — of the same kind 
— as the disease of her own Lucy. And yet that assumption was 
made, unless the matron carried her "propensity" to the point of 
recommending it for every case of illness in the village. Stated 
positively, inference from one case to other cases (which is a most 
important form of inference, being, as will be shown later, of the 
essence of the inductive function), 2 is grounded only through the 
intervention and intermediation of general propositions. Examina- 
tion of the two cases of illness in question is required to establish 
that they are similar or of the same kind. This examination is 
carried out by means of analytic comparison of both cases, a com- 
parison that establishes agreements and differences by using opera- 
tions that institute affirmative and negative propositions in strict 
correlation with each other. Moreover, this analytic comparison 
is effected (when it yields a grounded conclusion) by the oper- 
ative use of a conceptual apparatus of if-then propositions: If 
diphtheria, then certain characteristic traits; if typhoid, then cer- 
tain others; if measles, then certain others, and so on. Moreover, 
the conceptual apparatus is adequate only if the if-then proposi- 
tions that are employed form the content of a disjunctive system 
of propositions, theoretically (though not in practice) covering all 
possible cases of illness in such a way as to provide the procedural 

2 See Chap. XXI. 



268 THE STRUCTURE OF INQUIRY 

means of identifying and demarcating any case of illness whatever. 
For these reasons it was stated above that inference is made from 
one case to other cases only by the intermediary of general propo- 
sitions, instead of saying by a single general proposition. For 
there is the proposition that this case is of a kind, and there is the 
generalization of the if-then form which is required to ground the 
proposition about a kind. 

It will be noted that it is not denied that we do infer from one 
case to other cases. What is affirmed is that such inferences have 
logical standing — or are grounded — only as the inference takes 
place through the mediation of propositions of the generic and of 
the universal form. 

III. The Nature of Generic Propositions. Every proposition 
that involves the conception of a kind is based upon a set of 
related traits or characteristics that are the necessary and sufficient 
conditions of describing a specified kind. These traits are se- 
lectively discriminated by observation out of the total perceived 
field. What is the criterion upon which some traits are taken and 
others are omitted and rejected? From the standpoint of ex- 
istence, independently of its subjection to inquiry, there is no 
criterion. Everything in the world is like everything else in some 
respects, and is unlike anything else in other respects. From the 
existential point of view, comparison can form an infinite number 
of kinds and there is no ground whatever in any situation why one 
kind rather than another should be formed. For example, there 
are persons who have the quality of being cross-eyed, of being bald 
and being shoemakers. Why not form a kind on the basis of these 
qualities? The answer is that such a set of conjoined traits is 
practically worthless for the purpose of inference. This set of 
traits has no evidential value in respect to inferring other traits 
that are also conjoined but not observable at the time. It leads 
nowhere in inquiry. 

Such a conjunction of qualities as viviparous, warm-blooded 
and lung-breathing is taken, on the other hand, to describe the 
kind mammalian, because and only because this conjunction of 
characteristics promotes and controls extensive inference. It per- 
mits grounded conclusions to be made regarding singulars. For 
singulars are affirmed or denied to be mammals according as to 



GENERIC AND UNIVERSAL PROPOSITIONS 269 

whether this conjunction of traits is or not found to exist upon 
observational inquiry. If it were not for the conception of related 
traits, the inquirer would not know what to look for or how to 
estimate what he found. The set of traits also enables inferences 
to be made regarding relations of kinds. The traits selected fall 
within, through additive determinants, the set of traits which de- 
scribe the kind vertebrates, and is such as to enable demarcation to 
be made between the kind mammals and other kinds such as 
fishes. There was a time when the traits, walking, swimming, 
creeping and flying, were believed to provide the ground for iden- 
tifying and differentiating diverse kinds of living creatures. In 
the continuum of experiential inquiry, it was found to be both 
too wide and too narrow. It put insects, birds and bats in one 
and the same kind; fish and seals in another kind; reptiles and 
worms in a third kind. Scientific inquiry showed that, on the 
contrary, seals, birds and reptiles should be included in one in- 
clusive kind, because the traits by which that kind is descriptively 
determined enable inference to be ready and secure from case 
to case when they are found by directed observation to exist and 
sets barriers to inference when they are not found. 

The theory which has been most generally current (or at least the 
most popular notion) about the formation of general conceptions 
is that they are formed by processes of comparison which extract 
elements that are common to many cases and drop out those that 
differ. The point already made, namely, that formation of kinds 
is rendered purely arbitrary, since everything is like and unlike 
other things, applies to this view. A more important objection 
in the present connection is that it puts the cart before the horse, 
taking for granted the very thing that ■ is to be accounted for. 
Common qualities are already general qualities. For example, it 
is said that we form the general conception of a horse by compar- 
ing horses and taking the residuum of qualities they have in com- 
mon. But generalization has already been effected when the 
singulars are adjudged to be horses. 

If sound generalizations could be formed by placing, mentally, 
a number of singulars in a row and then throwing out unlike 
qualities until a number of "common" qualities remains, institution 
of kinds and of general conceptions would be an ultra-mechanical 



270 THE STRUCTURE OF INQUIRY 

and easy operation. One only has to consider the traits that de- 
scribe a kind in scientific inquiry to note that their institution is an 
arduous process, and does not proceed in the way that is here 
criticised. For scientific kinds, say that of metals, are instituted by 
operations that disclose traits that are not present to ordinary 
observation but are produced by operations of experimentation, 
as a manifestation of interactions that are taking place. For only 
qualities that are capable of being treated as signs of definite in- 
teractions facilitate and control inference. 

We are thus brought back to the thesis that the traits which 
descriptively determine kinds are selected and ordered with ref- 
erence to their function in promoting and controlling extensive 
inference. In other words, while every characteristic trait is a 
quality, not every quality is a trait. No quality is a trait in and 
of itself, or in virtue of existence. Qualities are existential and are 
produced and destroyed by existential conditions. For a quality 
to be a trait it must be used as an evidential sign or diagnostic 
mark. The very fact that qualities as traits are used to direct and 
to control inference is the reason why their fitness to perform 
the signifying function, to serve as evidential, is and must be itself 
a matter for careful investigation. 

We habitually employ qualities as signs although we do not 
habitually or "naturally" investigate their qualifications to be so 
taken and used. As a rule only artists and those of strong esthetic 
inclinations pay much heed to qualities as qualities. A red light 
on a street corner is a traffic signal; except in this function little or 
no attention is paid to its intrinsic quality. Moreover, the quality 
as an existence is constantly changing. It varies with atmospheric 
conditions, with changes of sunlight, with the distance and optical 
apparatus of the percipient, etc. It is constant and uniform only 
in its function. Variations in its quality as existential are indif- 
ferent—until they pass a definite limit— to its function as a stop- 
signal. 

It follows that the view that qualities are themselves general, as 
much so as relations and relationships, is as logically fallacious as 
is the doctrine that generals are determined by selection of "com- 
mon" qualities. Nothing more intrinsically unique and non- 
general than a quality as an existence can be imagined. The 



GENERIC AND UNIVERSAL PROPOSITIONS 271 

actual red of the traffic light is always varying, for existentially it 
is a manifestation of a vast complex of changing conditions. The 
function and only the function of a quality in grounding inference 
is constant and general. 

IV. The Nature of Universal Propositions, As has been said, 
the existential basis of a universal proposition is a mode of action. 
A universal proposition is not, however, merely a formulation of a 
way of acting or operating. It is such a formulation as serves to 
direct the operations by means of which existential material is 
selectively discriminated and related (ordered) so that it functions 
as the ground for warranted inferential conclusions. In other 
words, a content of a proposition has the form of universality in 
virtue of the distinctive function it performs in inquiry. Ways 
of acting are, as has been pointed out repeatedly, at first practical 
and actual. Through symbolization of propositional formulation 
they represent possible ways of action. Entertained and developed 
as possibilities of ways of acting which are existentially general 
(because they are ways and not singular acts or deeds) they acquire 
logical form. 

In a universal proposition, possibility of a mode of operation 
is expressed in an if-then form. If certain contents, then neces- 
sarily certain other contents. Traditionally, the if clause is called 
the antecedent and the then clause the consequent. But the rela- 
tion is purely logical, and the terms "antecedent" and "consequent" 
are to be understood in a logical, not in an existential sense. 
When an if-then proposition is formed in the process of delibera- 
tion about a specific matter of conduct, the two words have a more 
literal sense. "If I first do this, then certain consequences may 
be anticipated to follow." The relation in question is one of tem- 
poral priority and consequence. In the proposition, "If an act 
of trespassing, then liability to a penalty," the terms are abstract 
and the relation is non-temporal and non-existential, even though 
the contents, the ideas of trespassing and penalty, have indirect 
existential reference. When it is said "If a plane figure is a tri- 
angle, then the sum of its three interior angles is equal to two right 
angles," not only is the relation non-existential, but the contents 
are free from any prescribed existential reference even of the most 
indirect sort. In such a proposition there is not even a semblance 



272 THE STRUCTURE OF INQUIRY 

of antecedent and consequent even in a logical sense. The mean- 
ing would be the same if the proposition read "If the sum of the 
three interior angles of a plane figure is equal to two right angles, 
the plane figure is a triangle." 

In neither of the two cases cited does one clause follow from 
the other. For in their necessary interrelation they present the 
analysis of a conception into its integral and exhaustive contents. 
Hence it is misleading to say that one clause implies the other; 
not only because implication holds between propositions, not be- 
tween clauses, but because such a statement obscures from view 
the primary logical consideration — namely, that the two clauses 
represent the analysis of a single conception into its complete and 
exclusive interrelated logical constituents. For this reason a uni- 
versal hypothetical proposition has the form of a definition in its 
logical sense. Thus the proposition "If anything is a material 
body, it attracts other material bodies directly as its mass and 
indirectly as the square of the distance" may read equally well 
in the linguistic form "All material bodies, etc." It is a (partial) 
definition of being a material body. It expresses a condition which 
any observed thing must satisfy if the property "material" is 
groundedly applicable to it. On the other hand, if things are 
found that on grounds provided by other universal propositions are 
determined to be material which yet fail to answer to the require- 
ments prescribed by the proposition quoted, then one or other of 
the involved universal propositions must be revised and re- 
formulated. 

The foregoing paragraphs are intended to show (1) what is 
meant by the functional character of the universal proposition and 
(2) in what special way it is functional. This special way may 
be restated as follows: A universal proposition prescribes the con- 
ditions to be satisfied by existential material, so that if singular it 
is determined to be one of a specified kind, or if a kind, it is in- 
cluded in and/or is inclusive of certain other specified kinds. It 
accomplishes this function by means of actual execution of the 
mode of operation which as a proposition it formulates. For an 
actualized operation is performed upon existential conditions and 
has consequences in the literal or existential sense. Simple agree- 
ment of these actual consequences with the content of the 



GENERIC AND UNIVERSAL PROPOSITIONS 273 

apodosis clause of the hypothetical universal is not, however, as 
already explained, a complete test of the hypothesis. The actual 
consequences must be shown, as nearly as possible, to be the only 
ones which would satisfy the requirements of the hypothesis. In 
order that determination of this mode of satisfaction can be ap- 
proximately attained, the universal in question must be one of a 
system of interrelated universal propositions. A universal propo- 
sition which is not a member of a system could, at the most, only 
produce consequences that agree with the conditions it prescribes, 
without excluding the possibility of their also agreeing with condi- 
tions prescribed by other conceptions. 

V. The Conjugate Relation of Universal and Generic Proposi- 
tions: Implication and Inference. In the previous chapter it was 
said that "category" would be employed to designate the concep- 
tions which are formulated in universal propositions instead of the 
word class, since the latter word is also used to denote generals of 
the form of kinds. Every conception which functions as repre- 
sentative of a possible mode of operation may be called a category. 
Although in the history of philosophy, the word has been used 
to a large extent to designate only the conceptions that were taken 
to be ultimate (even so with little regard to their operational 
nature) , yet ordinary language uses the word more widely. When 
it is said, for example (taking the example from a dictionary quo- 
tation), that "this object falls within the category of machines," 
something more is meant than that it is included within the kind 
machines. What is meant is that it exemplifies the principle or 
order of principles by which being machinery is defined. A cate- 
gory is the logical equivalent of what practically is an attitude. 
It constitutes a point of view, a schedule, a program, a heading or 
caption, an orientation, a possible mode of predication; as, in Aris- 
totle, to categorize is to predicate. Civil and criminal laws fall 
into kinds. But being civil or criminal law are categories. They 
are points of view from which certain forms of conduct are ap- 
proached and regulated. A law is a formula for treatment. It 
determines whether certain agents can be brought before a court 
and how they shall be treated if and when so brought. Principles, 
prudential and moral, are categories. They are rules for conduct. 
While rules may themselves fall into classes in the sense of kinds, 



274 THE STRUCTURE OF INQUIRY 

being a principle is not a kind but is a prescription for forming 
kinds and thus for determining whether a given action or line of 
conduct is of a specified kind. 

Once it is recognized that a universal proposition is a formula 
of a possible operation, the chief logical problem about such 
propositions concerns their relation with generic propositions; that 
is, their relation with determination of the distinguishing traits 
which describe kinds. According to the view here stated, the 
relation is conjugate. Universals and generics bear the same rela- 
tion to each other in inquiry that material and procedural means 
sustain to each other in institution of judgment. Propositions 
about kinds and singulars as of a specified kind provide the subject- 
matter that forms the logical subject of final judgment. Proposi- 
tions about the operations to be undertaken in order to effect the 
transformation of problematic subject-matter into a unified con- 
tinuous existential situation provide the predicational subject-matter. 

An operation not formulated in a proposition is logically un- 
controlled, no matter how useful it may be in habitual practice. 
For until it is propositionally formulated, there is no ground for 
determining what consequences or what aspects of ensuing con- 
sequences are due to it and what consequences are due to extraneous 
unformulated conditions. The universal hypothetical states the 
relation between the operation and its consequences, the conse- 
quences being taken as themselves of operative force in the con- 
tinuum of experience, not merely as final and hence isolated. 
Thus they bear the same relation to propositions arranged in 
reasoning or ordered discourse, that propositions about kinds do 
to promotion and regulation of inference. ¥ articular consequences 
do not of themselves lead on to further consequences. In delibera- 
tion, the "if" of any action proposed as possible will have for 
its "then" certain contemplated consequences. But what the further 
consequences of these consequences will be, remains a separate 
problem, and one readily lost from view, especially when the 
special consequences are agreeable. When the "consequences" 
are themselves possible operations, their formulation leads naturally 
to propositions about further operations with which they are re- 
lated, or to discourse, until in mathematical discourse there is no 
set limit to the possibility of ensuing operations. 



GENERIC AND UNIVERSAL PROPOSITIONS 275 

Recurring to the topic of conjugate relationship in its bearing 
upon the relation of generic and universal propositions, we have, 
first, the fact (already noted) that the operations which constitute 
the content of predicate subject-matter are such as determine 
evidential data. In the second place, the data which are thus 
constituted become the tests of operations already executed and 
the ground upon which new operations (or modifications of old 
ones) are suggested and executed. An executed operation first 
transforms antecedently existent material so that the material ob- 
tained becomes more indicative or signifying, and then this changed 
material calls for further operations, and so on until a resolved 
situation is instituted. In short, the raison d'etre of a given opera- 
tion is that by it there is brought about approach towards the 
existential consequences that constitute a resolved situation. Prop- 
ositional formulation of the operation in advance of its perform- 
ance is a necessary condition of satisfactory execution of this 
office. On the other hand, scrupulous discriminative observation 
of the consequences of its actual performance, together with 
comparison of these consequences with those which are hypo- 
thetically determined, tests the validity (relevancy and force) of 
the propositional formulation of an operation, and thus reacts, when 
needful, to modify the operation and the proposition that are sub- 
sequently employed. 

Stating this conclusion in formal terms: — No grounded generic 
propositions can be formed save as they are the products of the 
performance of operations indicated as possible by universal prop- 
ositions. The problem of inference is, accordingly, to discriminate 
and conjoin those qualities of existential material that serve as 
distinguishing traits (inclusively and exclusively) of a determinate 
kind. The distinguishing traits that were once taken to describe 
the kind metals were peculiar lustre, opacity, malleability, high 
density and tenacity. The traits were observable qualities pro- 
duced by the ordinary operations of the body, seeing, touching, 
etc., conjoined with activities of craftsmen in manipulating things 
for the ends of use and enjoyment. Valuable as the consequences 
of these activities were for strictly practical purposes, they failed 
to guide inquiry as inquiry. They gave no aid in searching for 
other metals than those ordinarily in use (then some seven in all); 



276 THE STRUCTURE OF INQUIRY 

they gave no aid in linking metals with non-metals in a common 
system of inferential conclusions; they did not even ensure ac- 
curate discrimination of a metal from an alloy. The net conse- 
quence was that, even from the standpoint of practical use, the 
art of metallurgy was restricted within narrow bounds. 

The transition to the present scientific conception of being 
metallic and the determination of the traits by which the kind, 
metals, and its subkinds (more than sixty) are described was 
brought about when the point of view changed. It changed from 
consequences connected with direct use and enjoyment to conse- 
quences brought about by interactions of things with one another, 
human intervention consisting of the experimental operations that 
institute these interactions. The result was that immediate sensible 
qualities lost the significance previously given them as distinguish- 
ing traits. For example, an important element in the present 
definition of being metallic is "affinity" or capacity for interaction 
with certain non-metallic substances, especially oxygen, sulphur 
and chlorine, together with the capacity of oxides thus produced 
to interact as bases with acids to form salts. Another element is 
high positive electric capacity. It is obvious that such traits 
could never have been extracted as were lustre and opacity from 
immediate sensible qualities, or as tenacity and malleability were 
from operations executed by artisans. The traits are such as to 
promote (1) determination of previously unrecognized metals; 
(2) accurate discrimination of subkinds; and, (3) above all, to 
relate inferences made about metals to inferences about all chemi- 
cal changes in that extensive system which constitutes chemical 
science. 

The illustration has been developed in some detail because it 
illustrates so clearly both the distinction and the relation of (1) 
definition and description; of (2) categories and kinds; of (3) char- 
acters and characteristics. In these distinctions, the first term in 
each of the three pairs refers to a possible operation of the nature 
of an interaction while the second refers to the existential conse- 
quences of the actual execution of the operation. As distinctions, 
they are inherently related. The relation is that of operations as 
procedural means to existential conditions as consequences. "If 
metallic, then certain specified characters; if iron, sodium, tungsten 



GENERIC AND UNIVERSAL PROPOSITIONS 277 

. . . then certain additional differential consequences." The defi- 
nition thus forms a rule for the performance of (1) an experimental 
operation and (2) for guiding further operations of discrimination. 
The latter are selective of special qualities as inclusive and exclusive 
evidential signs of subkinds within an inclusive kind. 

The illustration up to this point has put its emphasis upon the de- 
pendence of propositions about kinds upon the definition provided 
by universal hypothetical propositions. Were the actual historical 
development of the latter in the progress of physico-chemical in- 
quiry followed out, the conjugate role played by existential propo- 
sitions of kinds in testing and revising previous universal 
conceptions would be equally evident. The later conceptions of 
being metallic, being iron, etc., did not appear out of the blue. 
They were suggested by conclusions as to matters-of-fact already 
obtained. The conversion of the suggestion into a proposition 
prescribed further operations, which yielded new matters-of-fact, 
and hence new ideas in the continuum of inquiry, until, on one 
side, the present conceptions and definitions were arrived at, and 
on the other side, the present set of differential descriptions and 
kinds. In short, the relation between the two forms of the uni- 
versal and the generic is functional: it is exactly similar in logical 
status and function to the relation between the logical subject and 
predicate of final judgment. 

The distinction of forms that has been discussed is, then, that 
between propositions facilitating and regulating inference and 
those constituting reasoning as ordered discourse. The movement 
from one existential proposition to another through inference de- 
pends, as we have seen, upon non-existential universal propositions 
as an instrumental intermediary — a consideration which demands 
that there be scrupulous attention to formation of the universal 
propositions employed in discourse. But the movement of infer- 
ence cannot be identified with that of rational discourse without 
radical doctrinal confusion. Nor can either one of the two logical 
movements be identified with the application of the universal 
proposition to existential material. No amount of reasoning can 
do more than develop a universal proposition; it cannot, of itself, 
determine matters-of-fact. Only operational application can effect 
the latter determination. On the other hand, existential data can- 



278 THE STRUCTURE OF INQUIRY ^ 

not of themselves prove a universal. They can suggest it. But 
proof is effected by (1) the formulation of the idea suggested in 
a hypothetical proposition, and (2) by the transformation of 
data into a unified situation through execution of the operations 
presented by the hypothetical as a rule of action. ^ 

The condition to be satisfied in reasoning or discourse is con- 
stituted by the implicatory relation. Problems of discourse have 
to do with ascertainment of rigorous and productive implications. 
Inference, on the other hand, is conditioned upon an existential 
connection which may be called involvement. The problems of 
inference have to do with discovery of what conditions are in- 
volved with one another and how they are involved. 3 A person 
engaged in a business undertaking is involved with others in the 
conditions of the situation in which the undertaking is to be carried 
out. In a criminal conspiracy one person is involved with his ac- 
complices in certain activities and consequences. But the scope of 
involvement is not confined to personal cases. An increase in the 
supply of gold involves, usually, a decrease in its price and an in- 
crease in the price of other commodities. The sudden and excessive 
rise of the customary level of a river is involved in heavy rain storms 
and involves with its occurrence perils to life and property, im- 
passable roads, etc. An outbreak of bubonic plague involves a 
rise in death-rate with, perhaps, a campaign to exterminate rats. 
There is no need to multiply instances. Every case of the causal 
relation rests upon some involvement of existential conditions with 
one another in a joint interaction. The entire principle of func- 
tional correlations of changes rests upon involvements, as when, 
in the case of many substances, increase of heat is ground for an 
inference to their expansion; or when the volume of gases is said 
to be a function of pressure and heat. The essential consideration 
is that the relation is a strictly existential one, ultimately a matter 
of the brute structure of things. 

Reasoning and calculation are necessary instruments for de- 
termining definite involvements. But the relations of terms and 

1 owe the word "involvement" and explicit recognition of its logical import 
as the conjugate counterpart of implication to Dr. Percy Hughes. See his article, 
"Involvement and Implication," Philosophical Review, Vol. XL VII, (1938), pp. 
267-274. He was kind enough to show me the manuscript in advance of pub- 
lication. 



GENERIC AND UNIVERSAL PROPOSITIONS 279 

propositions within reasoning and calculation (discourse) is im- 
plicatory and non-existential while description of kinds is a matter 
of involvement. Because the universal hypothetical propositions 
which constitute ordered discourse arise from analyses of single 
meanings or conceptions, their constituents sustain a necessary 
relation to each other. But propositions about objects and traits 
which are involved with one another in some interaction have ref- 
erence to the contingencies of existence and hence are of some 
order of probability. Therefore, an indispensable factor of in- 
quiry is determination of the order of probability presented in any 
given case. The traits or characteristics which describe a kind 
are taken to go together in existence. The ground of their selec- 
tion is logical but the ground of their going together is existential. 
The ground is that, as a matter of existence, they do go together 
or are existentially so conjoined that when one varies the other 
varies. When no reason why they should go together is seen 
(such as forms the content of a universal hypothetical proposi- 
tion), the ground for selection of a given conjunction may prop- 
erly be called "empirical." In the degree in which the selection 
of a conjunction is determined by the operational application of 
a universal proposition (and this proposition in turn is one of a 
system of universal propositions which have been severally tested 
in experimental application) the probability of the validity of a 
given existential proposition is of a high order. But it never at- 
tains the status of inherent logical necessity. It remains a brute fact, 
even after a law has indicated why and how a proposition about 
the brute fact is fruitful in promotion and control of inquiry. 

On the basis of the distinction and relation of existential in- 
volvement and logical implication, the point already made about 
the conjugate connection of generic and universal propositions 
may be illustrated as follows: One who is convicted of being an 
accomplice in a crime is so involved with the principals as to be 
involved in the consequences of the crime. But the involvement 
in, say, the penal consequences, results only because of the defini- 
tions of "crime," "principal" and "accomplice" instituted in a 
given legal system of conceptions. These definitions are cate- 
gories set forth in if-then propositions. By application of these 
categories, the presence or absence of the conjunction of traits 



280 THE STRUCTURE OF INQUIRY ^ 

which indicates that a given action is of a kind involving specified 
consequences is decided. On the other hand, it is clear that the 
definitions and categories in question did not emerge from the 
blue, but were evolved and explicitly formulated in terms of con- 
ditions set by the need of dealing with actual cases of human action. 
As another example, one may scribble his name on a piece of 
paper and no legal consequences follow. But under conditions 
which are determined by an abstract definition, he may be held 
liable for payment of a given sum when he signs his name. 
Finally, the legal definitions and conceptions are evolved and are 
modified with respect to' their function in regulation of situations 
which existentially arise in the field of human relationships. Ef- 
fectiveness in regulation of human conduct is their final criterion 
of validity. 

The functional correspondence, or conjugate relationship, of 
involvement and implication, kinds and categories, characteristics 
and characters, generic and universal propositions, signifies, to sum 
up, that they represent cooperative divisions of function in the in- 
quiry which transform a problematic situation into a resolved and 
unified one. The internecine logical war between empiricists of 
the type of Mill and the school of rationalism will continue as 
long as adherents of the one school and of the other fail to recog- 
nize the strictly intermediate and functional nature of the two 
forms of propositions as cooperative phases of inquiry. But the 
needed recognition cannot be effected until the field of logic is 
taken to be as broad as that of controlled inquiry. The relations 
of terms and propositions in discourse is such as to make possible 
purely formal statements — purely formal in the sense that it is the 
very nature of ordered discourse to deal with possibilities in 
abstraction from existential material. But any theory of "pure" 
logic which assumes that forms of discourse necessarily constitute 
the total subject-matter of logic is arbitrary. Fundamentally, it 
makes the personal interest which actuates a particular logician or 
group of logicians the criterion for logical subject-matter. In ad- 
dition, it fails to provide the logical ground for discourse and its 
forms, and to provide a rational explanation of their applicability to 
existence, which remains a matter of a mysterious preestablished 
harmony between the possible— which is not efficacious — and the 
actual. 



Part Three 

PROPOSITIONS AND TERMS 



CHAPTER XV 

GENERAL THEORY OF PROPOSITIONS 



"Udgment has been analyzed to show that it is a continuous 
process of resolving an indeterminate, unsettled situation 
into a determinately unified one, through operations which 
transform subject-matter originally given. Judgment, in distinc- 
tion from propositions which are singular, plural, generic and 
universal, is individual, since it is concerned with unique qualitative 
situations. Comparison-contrast is, upon this position, the funda- 
mental operation by which re-determination of prior situations is 
effected; "comparison" being a name for all the processes which 
institute cumulative continuity of subject-matter in the ongoing 
course of inquiry. Comparison-contrast has been shown to be in- 
volved in affirmation-negation, in measurement, whether qualitative 
or numerical, in description-narration, and in general propositions 
of the two forms, generic and universal. Moreover, it is a 
complex of operations by which existential conjunctions and elimi- 
nations, in conjugate connection with each other are effected — not 
a "mental" affair. 

Propositions are logically distinct from judgment, and yet are 
the necessary logical instrumentalities of reaching final warranted 
determination or judgment. Only by means of symbolization (the 
peculiar differentia of propositions) can direct action be deferred 
until inquiry into conditions and procedures has been instituted. 
The overt activity, when it finally occurs, is, accordingly, intelli- 
gent instead of blind. Propositions as such are, consequently, pro- 
visional, intermediate and instrumental. Since their subject-matter 
concerns two kinds of means, material and procedural, they are of 
two main categories: (1) Existential, referring directly to actual 
conditions as determined by experimental observation, and (2) 
ideational or conceptual, consisting of interrelated meanings, which 

283 



284 PROPOSITIONS AND TERMS 

are non-existential in content in direct reference but which are 
applicable to existence through the operations they represent as 
possibilities. In constituting respectively material and procedural 
means, the two types of propositions are conjugate, or functionally 
correspondent. They form the fundamental divisions of labor in 
inquiry. 

A contemporary movement in logical theory, known as logical 
positivism, eschews the use of "propositions" and "terms," substitut- 
ing "sentences" and "words." The change is welcome in as far 
as it fixes attention upon the symbolic structure and content of 
propositions. For such recognition emancipates logical theory 
from bondage to preconceived ontological and metaphysical be- 
liefs, permitting the theory to proceed autonomously in terms of 
the contents and functions of propositions as they actually present 
themselves to analysis. In emphasizing the symbolic element, it 
brings propositions into connection with language generically; 
and language, while about things directly or indirectly, is acknowl- 
edged to be of another dimension than that which it is about. 
Moreover, formulation of logical subject-matter in terms of sym- 
bols tends to free theory from dependence upon an alleged sub- 
jective realm of "sensations" and "ideas" set over against a realm 
of objects. For symbols and language are objective events in 
human experience. 

A minor objection to the use of "sentences" and "words" to 
designate what have been called propositions and terms, is that 
unless carefully interpreted it narrows unduly the scope of symbols 
and language, since it is not customary to treat gestures and 
diagrams (maps, blueprints, etc.) as words or sentences. How- 
ever, this difficulty may be guarded against. A more serious ob- 
jection is that without careful statement, the new terminology does 
not discriminate between language that is adapted to the purposes 
of communication (what Locke called "civil" language) and 
language that is determined solely by prior inquiries related to the 
purposes of inquiry— the latter alone being logical in import. 
This serious difficulty cannot be overcome by considering sentences 
and words in isolation, for the distinction depends upon an intent 
which can be adjudged only by means of context. 

In so far as it is not determined in a given case whether the 



GENERAL THEORY OF PROPOSITIONS 285 

intent is communication of something already known, or is use of 
what is already taken as known as means of inquiry into the as yet 
unknown and problematic, fallacies in logical theory are bound 
to arise. Take, for example, the matter of subject-predicate. The 
grammatical subject is the subject-matter that is taken to be 
common, agreed upon, "understood" as between the communicator 
and the one communicated to. The grammatical predicate, is that 
which is taken to be in the knowledge or thought of the one 
giving information or advice, but not in the knowledge or thought 
of the receiver. Suppose the sentence to be "The dog is lost." 
The meaning of "the dog" is, or is supposed to be, common for 
all parties; that of "is lost" to be in possession of the speaker, and 
while relevant to the experience and beliefs of the hearer, not 
previously known by him. 

Now if the logical theory of the subject-predicate is taken over 
from grammatical structure, it is likely, in fact, practically certain, 
to be concluded that the material of the logical subject is some- 
thing already completely given independently of inquiry and of 
the need of inquiry, so that only the characterizations provided 
in predication have logically to be taken into account. Indeed, it 
is not too much to surmise that the direct movement from gram- 
matical to logical structure had much to do with the Aristotelian 
formulation of the logical subject-predication relation. It led, on 
the one hand, to the theory that the ultimate subject is always 
some ontological substance and, on the other hand, to the classic 
theory of predicables. Again, it may not be too much to surmise 
that the doctrine, which has been criticized, regarding the im- 
mediately given character of the subject-content of propositions is 
an inheritance from the translation of grammatical into logical 
form, carried out under the influence of an uncriticized psychology 
of sensory-qualities as something immediately presented. 

An even more serious objection is that logical positivism as 
usually formulated is so under the influence of logical formalism, 
derived from analysis of mathematics, as to make an over-sharp 
distinction between matter and form, under the captions of "mean- 
ing of words" and "syntactical relations." Now there is no 
question that logical theory must distinguish between form and 
matter. But the necessity for the distinction does not decide 



286 PROPOSITIONS AND TERMS 

whether they are or are not independent of each other: — -Whether 
they are or are not, for example, intrinsically related to each 
other in logical subject-matter and distinguishable only in the- 
oretical analysis. While sentences or language invite making a 
distinction between the meanings of the words constituting its 
vocabulary and syntactical arrangements, this fact but poses in 
a new way the old fundamental problem of the relation, or absence 
of relation, between matter and form, or meanings and syntax. A 
tacit or explicit assumption that the distinction proves the in- 
dependence of matter and form, identifying the logical simply 
with the latter, only begs the fundamental point at issue. 

Ultimately, in spite of the nominal rejection of all "metaphysical" 
principles and assumptions, the idea that there is a sharp distinc- 
tion, if not a separation, between form and matter, rests on a 
special purely metaphysical tradition. The admittedly formal 
character of mathematics does not prove the separation of form 
and matter; it rather poses that problem in a fundamental way. A 
more direct objection along the same line is that the identification 
of the logical with syntactical form is obliged to assume, as given, 
the distinctions between nouns, verbs, adjectives, prepositions and 
connectives, etc. No attempt has been made, and I do not see 
how one can successfully be made, to determine what words have 
the distinctive force postulated in the above classification (are 
nouns, verbs, etc.) without taking account of their meaning, which 
is a matter of material content. 

It would be absurd, of course, to hold that the separation just 
mentioned is inherently involved in the substitution of "words" 
and "sentences" for "terms" and "propositions." But the fact that 
in the present state of logical theory the substitution is associated 
with the notion of this separation affords a reason for using the 
older terminology. This reason is linguistically reinforced by the 
fact, already mentioned, that the word "sentence" as ordinarily 
used expresses the close of inquiry rather than its initiation or con- 
tinuing execution. The word "proposition," on the other hand, 
at least suggests something proposed, propounded for further con- 
sideration, and thereby something entering integrally into the con- 
tinuum of inquiry. 

The basic issue regarding the logic of propositions concerns the 



GENERAL THEORY OF PROPOSITIONS 287 

intrinsic conflict between the theory that holds to the intermediate 
and functional status of propositions in institution of final judg- 
ment, and the theories, traditional or contemporary, which isolate 
propositions from their contextual position and function in de- 
termination of final judgment. According to one variety of the 
latter position, judgment alone is logical and propositions are but 
linguistic expressions of them — a position which is consonant with 
the idea that logic is the theory of thought as mental Another 
variety holds that since judgment is a mental attitude taken to- 
wards propositions, the latter alone are logical in nature. Sharp as 
is the opposition between these views, both of them hold that 
judgment — and "thought" generally — is mental. Both of them 
stand, accordingly, in opposition to the position here taken, which 
is that inquiry is concerned with objective transformations of 
objective subject-matter; that such inquiry defines the only sense 
in which "thought" is relevant to logic; and that propositions are 
products of provisional appraisals, evaluations, of existences and of 
conceptions as means of institution of final judgment which is 
objective resolution of a problematic situation. Accordingly, 
propositions are symbolizations, while symbolization is neither an 
external garb nor yet something complete and final in itself. 

The view most current at the present time is probably that which 
regards propositions as the unitary material of logical theory. 
Propositions upon this view have their defining property in the 
property of formal truth-falsity. According to the position here 
taken, propositions are to be differentiated and identified on the 
ground of the function of their contents as means, procedural and 
material, further distinctions of forms of propositions being in- 
stituted on the ground of the special w T ays in which their respective 
characteristic subject-matters function as means. The latter point 
is the main theme of this chapter. But at this point it is pertinent 
to note that, since means as such are neither true nor false, truth- 
falsity is not a property of propositions. Means are either effective 
or ineffective; pertinent or irrelevant; wasteful or economical, the 
criterion for the difference being found in the consequences with 
which they are connected as means. On this basis, special proposi- 
tions are valid (strong, effective) or invalid (weak, inadequate); 
loose or rigorous, etc. 



288 PROPOSITIONS AND TERMS ^ 

Validity-invalidity is thus to be distinguished not only from 
truth-falsity but from formal correctness. Any given proposition 
is such that it promotes or retards the institution of final resolution. 
It cannot be logically adjudged, therefore, merely on the basis of its 
formal relations to other propositions. The syllogism "All satel- 
lites are made of green cheese; the moon is a satellite; therefore, it 
is made of green cheese" is formally correct. The propositions 
involved are, however, invalid, not just because they are "ma- 
terially false," but because instead of promoting inquiry they 
would, if taken and used, retard and mislead it. 1 

The basic division of propositions has been said to rest upon 
their functional place in judgment. I return to this point. 
Grounded judgment depends upon the institution of facts which 
(1) locate and circumscribe the problem set by an indeterminate 
situation and which (2) provide the evidence which tests solutions 
that are suggested and proposed. Such propositions determine one 
of the two main divisions of propositions, those of subject-contents. 
But grounded judgment also depends upon meanings or conceptual 
structures which (1) represent possible solutions of the problem in 
hand, and which (2) prescribe operations which, when performed, 
yield new data tending in the direction of a determinate existential 
situation. These are propositions of predicate-contents — the other 
main division. 

The subject-matter or content of the first main division of 
propositions consists of observed data or facts. They are termed 
material means. As such they are potentialities which, in interac- 
tion with other existential conditions produce, under the influence 
of an experimental operation, the ordered set of conditions which 
constitute a resolved situation. Objective interaction is the overt 
means by which the actualized situation is brought into existence. 
What was potential at a given time may be actualized at some 
later time by sheer change of circumstantial conditions, without 
intervention of any operation which has logical or intellectual 
intent as, when water freezes because of a specified change in 
temperature. But in inquiry a deliberate operation intervenes; 
first, to select the conditions that are operative, and secondly, to 

1 These remarks are not supposed to cover the whole ground the relation of 
form and matter. That topic receives more extended consideration later. 



GENERAL THEORY OF PROPOSITIONS 289 

institute the new conditions which interact with old ones. Both 
operations are so calculated that as close an approach as possible 
may be made to determining the exact kind of interaction, in- 
clusively and exclusively, necessary to produce a determinate set 
of consequences. The relation between interacting conditions and 
actualized consequences is general, and is functionally formal, 
because it is freed from reference to any particular space-time 
actualization. 

Potentialities are to be distinguished from abstract possibilities. 
The former are existential "powers" that are actualized under given 
conditions of existential interaction. Possibility, on the other hand, 
is a matter of an operation as such — it is operability. It is ex- 
istentially actualized only when the operation is performed not 
with or upon symbols but upon existences. A strictly possible 
operation constitutes an idea or conception. Execution of the 
operation upon symbolized ideational material does not produce 
the consequences constituting resolution of tension. It produces 
them, as indicated in the previous paragraph, only by operationally 
introducing conditions that institute a determinate kind of interac- 
tion. The idea of taking a drink of water, for example, leads to 
actual drinking only because it institutes a change in prior condi- 
tions — if only by pouring from a pitcher or turning a spigot to 
bring water into connection with a new set of conditions. From 
these preliminary general statements discussion proceeds to con- 
sideration of the different kinds of propositions which are the 
sub-classes of the two main kinds just described. 

I. EXISTENTIAL PROPOSITIONS 

1. Particular Propositions. Propositions of the kind called 
particular represent the most rudimentary form of propositions of 
subject-content. They are propositions which qualify a singular, 
this, by a quality proceeding from an operation performed by 
means of a sense organ — for example, "This is sour, or soft, or red, 
etc." The word "is" in such instances as these has existential force 
not that of the timeless (because strictly logical) copula. "This is 
sour" means either that the actual performance of an operation of 
tasting has produced that quality in immediately experienced 
existence, or that it is predicted that if a certain operation is per- 



290 PROPOSITIONS AND TERMS 

formed it will produce a sour quality. "This is soft" means that it 
yields easily to pressure and will not cause most other things to 
yield when applied to them. When it is said of this "It is bright," 
an actual consequence of physical interaction with light is indi- 
cated. In short, the proposition is particular not because it ap- 
plies to a singular but because the qualification is of something 
taking place at a definite here and now, or is of an immediate change. 
In the strictly particular proposition there is no ground for intimat- 
ing that the this in question will remain sour, sticky, red, bright or 
whatever. "Is" is a verb of the strictly temporal present tense; 
or, if it is an anticipation of what will happen, it refers to an equally 
transitory local time in the future. 

When the above propositions are called, as they sometimes are, 
Propositions of Sense Perception, there is confusion of the causal 
conditions under which the particular quality occurs with the 
logical form of the quality. For practical purposes it is highly im- 
portant to know the causal conditions under which anything be- 
comes hard, sour, or blue. Without this knowledge there are no 
means of controlling the occurrence of such qualities. But the 
logical import of a "particular" is determined by the strictly 
limited local and temporal occurrence of the quality in question. 
Hence such propositions represent the first stage in determination 
of a problem; they supply a datum which, when combined with 
other data, may indicate what sort of a problem the situation 
presents and thereby provide an item of evidence pointing to and 
testing a proposed solution. There are, however, instances in 
which the same linguistic expression has the force of a singular 
proposition — a form next discussed. In a given context of in- 
quiry, "This is sweet" may not mean that some particular change 
is occurring which needs to be taken into account in formulating a 
problem. For in a special context, it may mark the resolution of 
some problem, as for example, a problem in which discovery of 
something which will sweeten something else is the object sought 
for. When a linguistic form is separated from the contextual 
matter of problem-inquiry it is impossible to decide of what 
logical form it is the expression. 

2. Singular Propositions. Singular propositions are such as 
determine this to be one of a kind. Take the two possible meanings 



GENERAL THEORY OF PROPOSITIONS 291 

of 'This is sweet." When the proposition is particular, it in- 
dicates, as has been said, an immediate change that has occurred 
or is about to occur. The same expression when it presents the 
solution of a problem, means that "this" is one of the kind of 
sweet things: or that this has the potentialities which are properties 
of any sweet thing. The sweet quality is no longer simply a 
change which has occurred; it is a sign of a conjoined set of con- 
sequences that will occur when certain interactions take place. 
Take for example the propositions "He is cruel," or "He is kind." 
The qualification represented by "cruel" or "kind" marks a 
disposition to act in a certain way, not limited to a change occur- 
ring at a given time; what occurs at the time is being taken as 
evidence of the permanent traits which describe a kind. If the 
expression were phrased to read "He is a cruel -person" the presence 
of traits describing a kind would be obvious. 

Such propositions as "This is an elm tree," or "This is sugar, is 
granite, is a meteorite, etc.," unambiguously identify and demarcate 
a singular as one of a kind. It is not necessary here to repeat what 
has been said about the force of the conception or category of 
kind in promotion of grounded inferential conclusions. It may be 
necessary to point out that when an adjective, like "benevolent," 
"mammalian," has the same logical force as a common noun, there 
is postulated the existence of other qualifying characteristics in 
conjunction with the one explicitly stated. When it is said, "This 
is iron," iron clearly refers to traits not now immediately present, 
but which as potential consequences stand in conjunction with the 
immediately present quality of color or touch. Similarly, the 
difference between the propositions "He is (now and here) acting 
kindly" and "He is kind," is constituted by the fact that the latter 
involves inference from the immediate datum of change stated in 
the former to a set of traits not then and there observable. 

The singular proposition thus takes us back to what was said 
in the previous chapter regarding the continuum of judgment. The 
propositions "This has vitreous lustre; cannot be scratched by a 
knife; scratches glass; is not fused by a blowpipe; breaks with 
conchoidal fractures" are propositions which, taken separately, set 
forth special modes of change. Applied concurrently and cumula- 
tively to this they yield the set of conjoined traits describing the 



292 PROPOSITIONS AND TERMS __ 

kind quartz. (I) A change is not merely noted as a brute fact, 
but the conditions are noted under which it occurs. (2) These 
changes are found to be so involved with one another that, in spite 
of variations in the circumstances in which they present them- 
selves, the presence of one is a valid sign that the others will present 
themselves if specified interactions occur. Similarly, the proposi- 
tion "This turns litmus paper red," of and by itself, records simply 
an isolated observation. In the course of cumulative progressive 
inquiries yielding other propositions about this, the proposition 
"This is an acid," (i.e., is one of a specified kind) is warranted. 
We are thus enabled to make definite the logical differences be- 
tween quality, characteristic trait, and property which have 
previously been noted. "Turning paper red," is, as the object of a 
particular observation, a quality. As enabling reasonably safe 
inference to be made as to the occurrence of other qualities under 
certain conditions, it is a distinguishing trait or characteristic de- 
scriptive of a kind. It becomes a property when it is determined 
by negative as well as positive instances to be a constant dependable 
sign of other conjoined characteristics. It then belongs inherently 
to all cases of the kind. 

Propositions of the class under consideration are often termed, 
in contemporary logical texts, propositions of membership in a 
kind. Membership, however, implies an articulation which is not 
involved. Propositions that "This is of specified kind," constitute 
"this" a case or representative of a kind, a specimen, rather than a 
member. 2 In one direction, determination of a singular as one of a 
kind involves a limitation of the singularity of this. It is no longer 
taken in its full qualitative existence, but is reduced to a character- 
istic which promotes identification and demarcation of it as of 
a kind. In another direction, namely, that of the range of grounded 
inferences that may be drawn, the limitation is conjugate with 
widening. Ordinary linguistic form is here, as in so many other 
instances, not a safe guide. "Paul was a Roman citizen," may 
merely state a particular historic fact, but in the context in which 
it was once uttered it signified that he was a representative of a 
kind of citizenship which carried with it certain rights. A mere 

2 The bearing of this distinction upon the concept of extension is considered 
below: See Chap. XVIII. 



GENERAL THEORY OF PROPOSITIONS 293 

succession of particulars cannot, therefore, determine that an 
existence is one of a kind. The particular changes that occur must 
have representative capacity. This fact is fatal to the assumption 
often made that a quality like red and hard, is inherently general 
or universal. It becomes such in cumulative inference in the 
continuum of inquiry; that is, when determined to be capable of 
application to an indefinite number of singulars not actually 
present. In and of itself it is particular to the point of uniqueness. 

Reference has been repeatedly made to contextual "conditions" 
as necessarily required for determination of the conceptions of 
characteristics, potentiality, and inference. The specific nature 
of these conditions is usually "understood" or taken for granted. 
Even in scientific inquiry and inference they are never completely 
stated. For a complete statement is impossible since it would have 
to exhaust practically everything. Standardized conditions are 
postulated, and are explicitly stated because, and as far as, they have 
differential effect. There are certain organic conditions under 
which sugar will not taste sweet and certain material conditions 
under which it will not sweeten another material. Only in special 
cases, is it necessary to state the conditions which cause conse- 
quences to be other than those normally postulated. For example, 
it is not safe to infer that a thing is sticky because it is sweet. But 
when differential conditions are adequately stated it is safe to 
infer that "This sweet thing is of the class of sticky things." 
Postulation, implicit or explicit, of the environing conditions that 
are required in a given case is equivalent to standardization of that 
set of conditions. 3 

3. Propositions of Relationship of Kinds, or Qeneric Proposi- 
tions. It is now generally recognized that the proposition "Atheni- 
ans are Greeks" is of different logical form from "Socrates is 
(was) an Athenian," and "This is iron" is of a different logical 
form from "Iron is a metal." The second proposition in each of 
the above pairs includes a lesser kind in a more extensive kind, as 
a species in a genus, while the first one of the pairs does not in- 
clude the singular in a class or kind. In them the kind, described 

3 1 owe to Dr. Nagel the observation that when formal symbols are employed 
to express this type of propositions, it is necessary to have a symbol standing 
for the postulated standardized conditions. 



294 PROPOSITIONS AND TERMS 



by means of specified traits, serves to identify and demarcate the 
singular, so that from directly observed characteristics other char- 
acteristics, not then observed or observable, may be inferred under 
given conditions. The membership of a kind in another kind not 
only extends enormously the number of characteristics that are 
inferable, but, what is even more important, it orders observed and 
inferred traits in a system. From the proposition "Roses are 
monocotyledonous angiosperms," it can be inferred that any ob- 
ject which is a rose has two seed leaves; that the parts of its flowers 
are not arranged by threes; that its leaves have reticulate venation, 
etc. And the wide range of inference is based upon general prin- 
ciples and not simply upon special observations. 

This extension of the range of inference is then more than a fact 
of great practical importance, although it is that. It has definite 
logical import. For it reacts to determine the ground upon which 
conjoined characteristics are employed to describe any one of the 
kinds in question. It is not enough to select traits which permit 
inference within the limits of the specific kind directly involved. 
The traits must be selected and ordered so that as far as possible 
there will be a series of kinds each included in another until the 
most inclusive kind is reached. Not only are barriers to special 
inference broken down, but the extension of the range of inference 
depends upon formation of kinds in systematic relation to one an- 
other. Such systematization is one of the chief differences between 
common sense and scientific kinds. It is this systematic serial re- 
lationship which renders the category of membership or inclusion 
applicable to included kinds and not to the case in which a singular 
is simply identified and demarcated as one of a kind. The proposi- 
tion of a relation of kinds thus provides the logical ground of the 
singular proposition. For in the proposition of the form "This 
is one of a kind," there is implicitly postulated that there are 
other kinds related to the one specified. For characteristics which 
suffice to ground the reference of this to a kind must be such as to 
demarcate it from other kinds. The adequate grounding of such a 
proposition demands, accordingly, that related but excluded kinds 
be determinately established. This condition is satisfied when 
(1) an inclusive kind is determined, and (2) when the differentia 
are ascertained which exclusively mark out included kinds from 



GENERAL THEORY OF PROPOSITIONS 295 

one another: — in other words, a set of conjoined affirmations- 
negations. 4 

Otherwise, the characteristics which are used to describe a kind 
may be such as either to overlap (and thereby the reference of the 
object or objects in question to another kind is possible) or else the 
characteristics taken are insufficient to justify reference to the kind 
specified: that is, they are too wide or too narrow. For ex- 
ample, when bats were assigned to the kind, birds, and whales to 
the kind, fishes, the characteristics of flying and swimming re- 
spectively were both too broad (inclusive) and too narrow (ex- 
clusive) to warrant the reference that was made. Only when 
coordinate kinds are determined, together with their differentia, 
and their subordination to (inclusion in) a more extensive kind, 
are logical conditions satisfied, and only then can inference pro- 
ceed warrantably in the case of singular propositions. 

The consideration that propositions of one of a kind and of a 
relation of kinds are related to inference is equivalent to surrender 
of the old system of rigid taxonomy; i.e., "classificatory" systems. 
As long as kinds were supposed to be ontological species marked 
off in nature, rigid taxonomic classification was inevitable. The 
substitution for such schemes of flexible relational kingdoms, 
orders, families, species, varieties, etc., in zoology and biology, was 
equivalent to determination of the relation of kinds on the ground 
of relationship to regulated systematic inference. The immediate 
effect of destruction of the idea of fixed natural species was, how- 
ever, logically disintegrative. For it led to the idea, which still 
obtains in traditional empiristic logical theory, that all division into 
related kinds is merely a matter of practical convenience without 
intrinsic logical meaning. However, the discovery of progressive 
derivation, through differentiation under environing conditions, 
from a common ancestor, institutes an objective basis. In com- 
parison with the theory of fixed species it marks restoration of an 
objective status of classification but upon a different basis. Ex- 
ternally, the difference is marked by the substitution of belief in 
"the origin of species" for the assumption of fixed natural kinds. 

The logical equivalent of this change is a working postulate— 

4 See Chap. X pp. 183-4, 197-8 and, below, the discussion of conjunctive- 
disjunctive functions, Chap. XVIII. 



296 PROPOSITIONS AND TERMS 

viz., that the arrangement of singulars in the classes which 
promote and control extensive inference, is that of genetic der- 
ivation or descent, where differentiation into kinds is conjoined 
with differentiations of environing conditions. On this basis, 
reptiles, for example, are found to be more nearly akin to birds 
than to toads and salamanders, with which they were originally 
classified. This change to a genetic principle of classification is 
identical, logically, with the shift from antecedents to consequences 
as the ground upon which to institute the conjunction of character- 
istics which describe kinds. It conforms to the emphasis placed 
upon interaction of conditions. 

At this point, it is well to revert to the basic difference between 
generic propositions and universal propositions. It is not neces- 
sary here to repeat in detail what has been said about the ambiguity 
of "all" as sometimes having existential reference, in which case 
it represents an inference having at best a high order of probability, 
and sometimes having non-existential reference, when it stands for 
a necessary relation which follows, by definition, from analysis of 
a conception. 5 It is, however, in place to say something here 
about the contrast of the present logical interpretation and the 
traditional theory which holds that all propositions, except rela- 
tional ones, are either classificatory or attributive, according as they 
are taken, at will, in "extension" or "intension." The contrast goes 
back to the fact that the position of the text affirms that all 
existential propositions are concerned with determination of 
changes; specifically of those changes which effect the transforma- 
tion of an indeterminate unsettled situation into a determinate 
unified existential situation. Initial particular propositions, as we 
saw, are concerned with particular changes determined for the 
purpose of locating the problem set by a doubtful situation. These 
changes are linguistically expressed by verbs of action such as 
tastes, touches, hears, breaks, hits, runs, loves, moves, grows, stays, 

5 It would not, however, be hard to show that texts which recognize and 
explicitly state this ambiguity nevertheless tend to carry over the kind of 
generality marking the subject-matter of non-existential propositions to the 
subject-matter of existential generalizations. In this case they treat the prob- 
ability property of the latter as a failure in logical status, since genuine logical 
form is defined on the basis of that necessity which is the property of rational 
discourse or the inter-relations of conceptions. Induction then becomes a 
logical scandal, since it is practically necessary and theoretically illegitimate. 



GENERAL THEORY OF PROPOSITIONS 297 

etc., and then by adjectives which indicate the consequences of 
the change effected by the action expressed by a true verb. In 
the form in which a relation of kinds is determined, the changes in 
question become modes of interaction. The traditional interpreta- 
tion of the classificatory nature of propositions rests upon ignor- 
ing connection with change. There is substituted for change a re- 
lation designated by is in the sense of a logical (non-existential) 
copula. "Jdm runs," (expressing change) then becomes "John is 
a runner." "John runs," even when it takes the form "John is 
running," refers to some definite time and place; "is" in "is run- 
ning" is a verb of action having tense and spatial reference; he is 
running now and here. "John is a runner," in the traditional 
interpretation, subordinates the singular, John, to a kind. It would 
hardly be a valid proposition unless John was by profession one 
who engaged in the sport of racing or at least showed a disposition 
to run on every suitable occasion. 

Take again the proposition "John gives an apple to James." 
He does it at a certain time and place. The proposition marks an 
existential change then and there going on. The change may never 
have taken place before and may never occur again. But the 
proposition is often translated into the following: "John is a donor 
of an apple to James." The change is not merely verbal. It marks 
a shift in logical form. The relation of donor and donee is generic, 
and hence free from limitation to a specified time and place. Taken 
literally, the proposition in its translated form indicates that John 
makes a business of giving apples to James or at least that he is 
disposed to do so. Suppose, for example, we take the proposition 
"John Smith made a will in favor of George Jones." This is an 
act (change) which takes place at a given time and place. There 
must be witnesses, observers, of its occurrence. The relation be- 
tween testator and legatee is, however, generic. Statement of the 
special act in terms of the relation brings the former within a 
system of legally defined categories whose application determines 
differential consequences. Apart from being one of the kind 
which is determined by legal categories, the special act could not 
be described as making a will. It would still be something which 
occurred at a given time and place, but might not be differentiated 
from scribbling one's name on a piece of paper. 



298 PROPOSITIONS AND TERMS 

In contrast with propositions just discussed, propositions affirm- 
ing a relation of kinds such that one kind is included along with 
others in an extensive kind are, truistically, "classificatory." But it 
is a serious logical confusion to extend this classificatory character 
to singular propositions in intension as well as extension, when, 
truistically, they are supposed to be attributive. For logical con- 
fusion of forms occurs when it is concluded from the attributive 
character of the characteristics which determine a relation of kinds 
that "sweet" in the proposition "This is sweet," is attributive. Sweet 
is in no sense necessarily an attribute of "this." It may mark simply 
a particular change that has occurred, is now occurring, or that 
will occur at some particular time-place. So far, there is a restate- 
ment in other language of a point already made. We come to an 
additional point of logical importance when it is noted that the 
interpretation of all propositions in terms of classification or at- 
tribution (and of extension and intension) obscures their inter- 
mediary and functional nature. 

The proposition "Iron is a metal" certainly means that the kind 
designated "iron" falls within the kind designated "metals." Or, 
stated attributively, it certainly means that the interrelation of 
characters by which being metallic is defined applies also to the 
interrelation of characters by which being iron is defined. But in 
whichever of the two ways the proposition is read, the proposi- 
tion is instrumental to inference. And the sole logical ground for 
discrimination of the logical form thus presented from that of 
propositions such as "This is iron," resides in the kind of inference 
promoted. When an artisan determines "This is iron" he can in- 
fer what consequences will ensue if he treats it in a certain way: 
for example, that if he heats it, it will become soft enough to work. 
But the propositions "Iron is a metal" and "if anything is metallic 
it is a chemical element" are, as pointed out, grounds for inference 
of a different order. 

4. Contingent Conditional Propositions. There is a type of 
propositions which are linguistically hypothetical and which never- 
theless refer to singulars. The proposition "If this drought con- 
tinues the harvest will be very poor" and "If that is dropped, an 
explosion will probably follow" refer to existential changes which 
are taken to be involved with one another. The same thing holds 



GENERAL THEORY OF PROPOSITIONS 299 

of such a proposition as "If the rain continues, the scheduled ball 
game will be postponed." Such propositions exemplify a very 
common type of proposition. They are marked by the words "If- 
then." But, as was remarked in an earlier chapter, in such cases 
there is postulated an existential connection between existential 
conditions in which the terms "antecedent" and "consequent" 
have literal or existential meaning. The drought, the bomb, are 
now in existence; if something happens (designated by "continues" 
and "dropped"), then certain physical results will follow in the 
temporal sense of follow. The connection is contingent and the 
propositions are of some order of probability. They are, more- 
over, preparatory. They are of the nature of advice or warning 
with respect to getting ready for future probable occurrences. 
"Get ready for a shortage of grain"; "Don't drop that thing unless 
you want an explosion to result"; "Don't take a trip to the ball 
park until you are sure about the weather." They are marked 
off from abstract universal hypotheticals in form, since they have 
specific spatio-temporal reference. 

Logically speaking, such propositions are means of determining 
a problem. Take propositions of wider import, such as "If the 
Phaedo is historical, Socrates believed in the immortality of the 
soul," and "If the dialogue is dialectical, it does not necessarily fol- 
low that Socrates personally was committed to that belief." 
The propositions decide nothing. But they indicate a problem. 
How far is Plato, in his dialogues in general and in this dialogue in 
particular, purporting to recount actual conversations that took 
place at definite dates and places? How far is he using the figure 
of Socrates to develop certain conceptions of his own? The 
propositions thus direct inquiry into channels where evidence for 
the solution of this problem may, it is hoped, be found. Both 
problem and solution, if the latter be found, are existential in 
reference. 7 

5. Matter-of-fact or Contingent Disjunctive Propositions. The 
necessity for determination, through negation and exclusion, of the 

6 The first of these propositions is taken from Joseph, An Introduction to 
Logic, p. 185. 

7 The difference in logical form from universal if-then propositions indicates 
the necessity for differential symbols when formal symbols are employed. "If 
A 9 then B" is wholly indeterminate in this respect. 



300 PROPOSITIONS AND TERMS 



characteristics that describe other kinds included along with the 
given kind in question in an including kind, has been pointed out. 
Observance of this condition generates existential disjunctive 
propositions. That "Iron is a metal" is not a proposition grounded 
simply by discovery that it possesses certain characteristics also 
found in tin, copper, lead, mercury, zinc, etc., for it is not grounded 
until the distinguishing characteristics which exclusively dif- 
ferentiate iron as a kind from those that describe other metals 
have been determined. Otherwise, iron might conceivably be an 
alloy like brass or bronze, since without exclusive or negative 
propositions not all the conditions are satisfied which are imposed 
by the definition of being a metal; — for example, that of being a 
chemical element. That a kind is ivarrantably included in another 
kind is thus dependent in logical ideal upon the formation of a 
set of exhaustive disjunctive propositions, such as "Metals are 
either ... or ... or ... or .. , and these kinds are all the 
kinds of metals there are." 

The dots (. . .) in the last sentence are meant to suggest that 
such disjunctive propositions are materially conditioned and hence 
are contingent, since there can be no guarantee that the formal 
condition of exhaustiveness is satisfied. The spectroscope has 
widened the area of observation. But until everything in all 
universes and galaxies has been analytically observed there is no 
assurance that the list of metals is complete. And even if this 
condition were fulfilled, it would still be a matter of fact, not of 
theory, that the disjunction is exhaustive. Only on the ground of 
theory which would prove that the existence of other metals is 
logically impossible, because involving contradictions, would the 
disjunctives be otherwise than contingent. 

II. UNIVERSAL PROPOSITIONS 

1. Hypothetical Propositions. The organic condition of predi- 
cation is a mode of action, native or acquired, as in the case of a 
habit. A mode of active response, when it is inhibited from overt 
manifestation and expressed in a symbol, is a suggested meaning 
presenting a possible way of solving a problem. It retains its 
kinship with its organic source in standing for a way of active 
response, a way of dealing with existing conditions. It passes from 



GENERAL THEORY OF PROPOSITIONS 301 

the status of suggestion to that of idea (In its logical sense) only as 
it is developed in relations to other symbols; that is, only as its 
meaning is developed in relation with other meanings. The first 
stage in this process is explicit formulation of the suggested mean- 
ing: its conversion into a proposition. The propositional form ex- 
pands the idea into a relation of meanings. This expansion is not 
effected by conjoining or annexing an additional meaning to the 
original suggestion while leaving the latter unchanged. It con- 
sists of analysis of that which was first suggested. In an inde- 
terminate situation, certain observed data suggest the presence of a 
man at a distance who is beckoning. If some other meaning were 
then merely added on, the effect would be that meanings would 
be accepted as they occur. This is the road that leads to phantasy. 
Inquiry or critical examination, such as is required to transform 
what is suggested into a logical idea or a meaning, must of neces- 
sity be applied to the constitution or structure of the suggested 
meaning: such a statement is truistic. The inquiry resolves it into 
related terms: // a man, then certain other things which are in- 
herent constituents of being a man: that is, conversion of a con- 
ception into a definition. 8 

As soon as a meaning is treated as a meaning, it becomes a 
member of a system of meanings. This statement is implied in the 
remark of the previous paragraph that a meaning must be de- 
veloped in relation with other meanings. This development con- 
stitutes reasoning or rational discourse — where discourse is a matter 
of sequential implications rather than communication of some- 
thing already possessed. A universal proposition, in other words, 
has meaning as a member of a system not in isolation. The rela- 
tion of implication is an expression of this fact, so that the de- 
velopment of an expanded meaning or hypothetic universal in 
terms of implied propositions, is the determination of "what that 
meaning is. The emergence of contradictions, as in reductio ad 
absurdum, is proof that the original meaning was not what it was 

8 Among other things, this formulation is a safeguard against a current notion 
that the relation of antecedent and consequent is that of implication. Implication 
holds between propositions, not between constituents. The necessary relation 
obtaining between "antecedent" and "consequent" in the universal hypothetical 
is an expression of the fact that there is but one and the same meaning involved, 
the "antecedent" and "consequent" being taken to be its constituent parts. 
If the "taking" is correct the relation is (truistically or tautologically) necessary. 



302 PROPOSITIONS AND TERMS 

taken to be. The logical difference between universal and par- 
ticular propositions is sharply marked at this point. The latter 
are determinations of the data that set the problem to be dealt with. 
Different particulars, independent in their material content, are 
connected with one another in that they all have the same func- 
tion—that of logically determining a problem. In the earlier 
illustration, the determination 'This is quartz" occurs through a 
cumulative series of materially independent operations of observa- 
tion such as "This has vitreous lustre; it scratches glass but it is not 
scratched by a knife, etc." The force of these propositions is 
cumulatively evidential only in the degree in which their contents 
are materially independent, having no content in common with 
one another save "this." Exactly the opposite is the case with 
universal propositions. In the latter a break in community of 
meaning is a break in rigor of reasoning. 

It has previously been shown that universal propositions are 
formulations of possible operations. As long as the operations are 
not executed, the subject-matter of such propositions is therefore 
abstract or non-existential. Take the proposition "Only if men 
are free, are they justly blamed." Neither the existence of free- 
dom nor of just blame is affirmed. While it may be said that the 
existence of men is postulated, it is not implied nor is it expressly 
affirmed. The relation affirmed between freedom and just blame, 
if it is valid at all, will still be valid if all human beings are wiped 
out of existence. Freedom, justice and blame designate abstract 
characters. Nevertheless, the proposition formulates possible 
operations which, if actually performed, are applied to the actual 
conduct of men so as to direct observations into the conditions 
and consequences of actual cases of blame. Apart from such ap- 
plication, the proposition represents merely an abstract possibility 
depending upon a definition of freedom and justice which, as far 
as existence is concerned, might very well be arbitrary. The 
proposition may hence be countered by the contrary proposi- 
tions "Only if men's actions are causally conditioned, can blame 
be effective, and only if it is effective is it justifiable." 

Save as the two propositions are employed to direct operations of 
inquiry to systematic observation of the facts of human conduct 
(with respect to the conditions and consequences of blame) is 



GENERAL THEORY OF PROPOSITIONS 303 

there any ground for deciding in favor of one of these abstract 
possibilities rather than the other. Reasoning or dialectic (leaving 
the subject of mathematics for later discussion) thus has ultimately 
the function of directing operations of observation to the de- 
termination of the existential data which test proposed possible so- 
lutions, contrary propositions being (as we have seen) means of 
delimiting the field of inquiry. 9 

An even more crucial instance is provided by hypothetical 
universals contrary to fact such as are constantly employed in 
science, as for example the proposition "If bodies interact with- 
out friction, then . . ." or "If a body moves upon impact of one 
body only without being affected by other bodies, then. . . ." The 
value of such propositions is proved by their constant use in scien- 
tific calculations. Upon any other theory than that of the ultimate 
connection of hypothetical universals with conduct of observa- 
tional experimental operations in inquiry, the proved utility of 
propositions contrary to fact presents an insoluble paradox. The 
attempt has been made to resolve the paradox by saying that while 
the propositions in question do not affirm anything of existence, 
they "ascribe to reality a character which is the ground of the 
connection stated in the hypothetical judgment." Regarding 
this mode of interpretation, it has been pertinently asked "How 
can there be the ground in the real universal of something which 
nevertheless does not exist?" 10 The seeming paradox completely 
disappears when it is seen that such propositions do not intend or 
purport to have reference to existence but to be relevant to inquiry 
into existence — a very different matter. 

There is indeed something of the nature of contrary ~to-factness 
in all definitions. For they are ideal as well as ideational. Like 
ideals, they are not intended to be themselves realized but are 
meant to direct our course to realization of potentialities in existent 

9 The formation of alternatives which are contrary to one another, as in the 
above instance, is required in order to conduct observations that yield negations 
or eliminations, while if negative propositions are neglected the final proposition 
is subject to the fallacy of affirming an antecedent because the consequent is 
affirmed. Dialectical reasoning, provided it proceeds disjunctively, can and 
should clarify the conceptions involved. But only systematic observation of 
cases of blame can decide which of two contrary abstract propositions in the 
disjunction can be converted into a valid proposition. 

10 Joseph, Op. cit., p. 185. 



304 PROPOSITIONS AND TERMS 



conditions — potentialities which would escape notice were it not 
for the guidance which an ideal, or a definition, provides. We 
may not think the better of the mathematical circle because it 
cannot be matched by figures that exist, nor worse of actual figures 
because none of them possesses the roundness defined in the 
mathematical conception. To sanctify the ideal and to disparage 
the actual because it never copies the ideal, are two connected 
ways of missing the point of the function of ideal and actual. A 
vision is not a scene but it can enable us to construct scenes which 
would not exist without it. To suppose that a vision is worthless 
unless it can be directly determined to be a scene is for those who 
take the idea seriously, the high road to pessimism, and for others 
the road to fantasy. To ignore or depreciate the ideal because it 
cannot be literally translated into existence is to acquiesce not only 
to things "as they are" — as is sometimes said — but also to things 
"as they are not" because all things that are have potentialities. 

Without retraversing ground already gone over, it may be 
pointed out that linguistic form, apart from content does not 
determine whether a sentence is logically about existential relation- 
ships or about abstract possibilities. Thus, "if grain is scarce, it 
is dear," may mean that in all known cases there is a conjunction 
of the characteristics of scant crops with high prices (both char- 
acteristics referring to actual occurrences), or it may mean that 
there is a necessary relation between the abstract characters 
scarcity and clearness. The ease with which the two forms of 
logical force are identified is explicable upon the basis of the con- 
jugate relation or functional correspondence already mentioned. 
Unless it can be shown as matter of theory that there is an inherent 
relation between scarcity and dearness, the observed conjunction 
between small crops of grain and high prices may be circumstantial 
and coincidental. Stated from the other side, uniformity of an 
observed conjunction instigates search for the reason of the con- 
junction, which, when found, is stated in a proposition of relation- 
ship of abstract characters, in this instance, scarcity and dearness. 

The conjugate relation of universal and generic propositions thus 
serves to explain an ambiguity in the meaning of empirical, and to 
throw light upon the logical relation of the empirical and the 
rational. In one sense, the more comprehensive one, empirical 



GENERAL THEORY OF PROPOSITIONS 305 

is Identical with being proved (by means of controlled observa- 
tional operations) to be existential. In this sense it is opposed to 
the merely ideational and merely theoretical. In a more restricted 
sense, empirical means that the subject-matter of a given proposi- 
tion which has existential reference, represents merely a set of 
uniform conjunctions of traits repeatedly observed to exist, with- 
out an understanding of <why the conjunction occurs; without a 
theory which states its rationale. In the latter sense only, is there 
opposition between the empirical and the rational. When the 
opposition exists, it sets a problem for further inquiry. It is a 
sign that propositions already formed do not satisfy the conditions 
which must be met in order to ground final judgment. Logical 
theories which fail to note the relativity of propositions to the 
given stage of inquiry attained, erect the distinction of empirical 
and rational into a rigid difference in the ontological natures of 
their respective subject-matters. The falsity of this interpreta- 
tion is shown in the fact that observed uniformity of conjunction 
of traits is in every scientific case a stimulus to the formation of 
conceptions (expressed in hypothetical propositions) which indi- 
cate a reason for the observed uniformity of conjunction. On 
the other hand, the suggested reason is but an abstract possibility 
until its formulation, through the intermediary of experimental 
operations has produced existential consequences. These opera- 
tions are conducted from a point of view different from those 
which yielded the previously observed conjunctions, since they 
are conducted to vary the conditions under which previous uni- 
formities were observed. Hence, even when consequences reached 
agree with the phenomena previously observed, the probability 
that the conjunction is inherent and not merely circumstantial is 
greatly increased, since the new consequences are produced under 
conditions of conceptual experimental control. The clinching evi- 
dence is provided to the degree in which, by elimination or pro- 
duction of negative cases, other abstract possibilities are ruled 
out. 11 

2. Disjunctive Universal Propositions. Disjunctive form, in the 
case of universal propositions, is not to be identified with disjunc- 

11 It is hardly necessary to point out that there is an ambiguity in the words 
rational and theoretical which is the counterpart of that attending empirical. 



306 PROPOSITIONS AND TERMS 



tion in the case of generic propositions. The propositions that 
triangles are equilateral, scalene or right-angles is not of the same 
form as the proposition that metals are either tin, zinc, iron, 
mercury. . . . The difference is related with the ambiguity in 
"included" and "including" which has already been noted. Singu- 
lar items are comprised in a collection. Singular objects indefinite 
in number, such that each and every one, having specified char- 
acteristics is one of a class (in the botanical and zoological sense 
of class) form or constitute the class of which they are of. To 
say that they are contained or included in it is but a back-handed 
way of saying they constitute it. They are certainly not contained 
existentially as pennies are contained in a box or cows enclosed in 
a field, nor are they contained as kinds are logically contained in 
a more extensive kind. To affirm that Mr. Franklin D. Roosevelt 
is "included" in the class of Presidents of the United States is 
only an awkward way of saying that he is one of the Presidents, 
past, present, and future, who make up the collection. For 
ultimately any class (as kind) is composed of an indefinite number 
of singulars. 

A kind is properly said to be contained in another wider kind 
whenever the characteristics which describe the wider kind are 
a conjoined part of the set of characteristics which describe every 
included kind, and are also such as to enable, through a series of 
negative and disjunctive propositions, all included species to be 
exclusively demarcated from one another. The contrast with 
inclusion of singulars in a collection is seen in the absurdity of 
the notion that the conception of the "presidential" kind will en- 
able different Presidents to be discriminated from one another. 
The relation of kinds to an inclusive kind and of included kinds 
to one another is suitably expressed by the traditional scheme of 
circles, the relation of the including genus to other genera being 
expressed by circles which lie entirely outside its boundaries. The 
sense in which "inclusion" applies to definitions and conceptions 
determines a different logical form. It cannot be symbolized by 
circles but may be symbolized appropriately by brackets or 
parentheses. Suppose it is a question of the definition of wealth in 
political economy. What shall be "included" in the conception? 
Shall wealth be defined in terms of utility as satisfaction of desire 



GENERAL THEORY OF PROPOSITIONS 307 

or as forwarding of purpose; or as exemption from "labor" in 
the sense of cost and sacrifice? Or, as power to command other 
commodities and services? There is here no question of kinds. 
But the conception or definition adopted will, when applied ex- 
istentially, decide what things fall within and what without the 
kinds of things that are wealth. Similarly, existential figures may 
be classified as kinds of plane figures or of triangles. But, mathe- 
matically, "triangle" means triangularity, an abstract universal or 
category. As has been repeatedly stated, there are not three kinds 
of triangles but three modes of being triangular. Hence in the 
case of what is "included" in an idea or definition, any division 
of being such-and-such, if it is valid at all, is necessarily exhaustive, 
while in the case of kinds it is contingent. In the case of univer- 
sal, to "include" means to be an integral part of an operative rule, 
which when applied determines what falls within the domain of 
operation. To exclude means to rule out, to debar; being a 
principle for determining inadrnissability in the abstract. Ex- 
haustiveness of disjunctions is, thus, a necessary character of ab- 
stract propositions. They must form an interrelated system. 

III. RELATIONAL PROPOSITIONS 

Logical theorists who retain as much of the Aristotelian logic 
as possible (although in a purely formalistic interpretation) criticise 
that logic because it recognizes only the subject-predicate form. 
They have shown the importance of relational propositions and 
of a logic of relatives. Relational propositions, like if-then propo- 
sitions are, however, of two forms that must be distinguished. 
"This (town) is south of that"; "that table is farther away than 
this stand"; "the book you want is to the right of where you 
are looking," are relational. But they are singular and of ex- 
istential reference. The word "is" in these propositions is the 
temporal verb, not the non-temporal logical copula. The relation 
is one of a spatio-temporal fact. Yesterday the table and stand 
and the books in question may have been differently situated with 
respect to that which is nearer or to the right of; they may be differ- 
ently placed tomorrow. While the relative position of towns is 
not so readily shifted, there is nothing logically necessary in their 
present space-relationship. This principle holds of all singular 



308 PROPOSITIONS AND TERMS 

relational propositions. For example, in the proposition "George 
is heavier (taller, darker, etc.) than James," heavier means weigh- 
ing more; taller means subtending more space in a vertical direc- 
tion. "Is" is not the logical copula for like all verbs of action it 
expresses a mode of action or interaction at a given time, just as 
north-south, right-left have to do with directions of movement. 
Logically speaking, there is no difference between the form of 
such propositions and the form of such propositions as "This is 
(growing, becoming) warm, red, soft, bright." They are particu- 
lar propositions. 

In other words (and this is the important consideration), all 
particular propositions are relational. They do not have a subject- 
predicate form save grammatically. "This is red" means, when 
it is analyzed from a logical point of view, that an object has 
changed from what it was, or is now changing into something 
else. It expresses a temporo-spatial connection as truly as do those 
which are relational in obvious grammatical form. Propositions 
of one of a kind are also relational. Their reference is not to a 
particular change taking place, but (as was shown earlier) to dis- 
positions or potentialities of change. "This is iron" means that 
this, under specifiable conditions, will interact in certain ways and 
produce certain consequences. Only grammatically is "this" a 
subject and "iron" a predicate. Its relational character is seen 
in the fact that what is expressed can be put in the passive voice 
"Certain specified consequences will be produced by "this? under 
certain conditions." The grammatical form can be changed with- 
out changing the sense, just as "James strikes John" is completely 
equivalent to "John is struck by James." 

Propositions about a relation of kinds are also relational, having 
no logical subject-predicate form. When it is said that "Iron is a 
metal" the proposition does not appear to be relational because we 
cannot convert it simply into "metal is iron." But the proposition 
as it stands is not logically a complete proposition. It does not 
indicate or even suggest its own grounds. At most it is either a 
sentence communicating information or is a proposition prelimi- 
nary to further inquiries. The complete proposition is "Iron is a 
metal possessed of such-and-such differential characteristics." Any 
metal having these specified properties is iron, so that the proposi- 



GENERAL THEORY OF PROPOSITIONS 309 

tion is logically, not verbally, a proposition regarding a relation 
of kinds. 

The relational character of universal hypothetical propositions 
is also obscured by the fact that as they are reached and formu- 
lated they are often not completely determinate. In consequence, 
affirming the "consequent" is not a ground for affirming the 
"antecedent" nor denying the latter a ground for denying the 
former. Obviously, certain conditions necessary for complete 
logical reciprocity and equivalence are lacking. But this lack is 
not due to the form of the universal hypothetical; it marks a failure 
of its contents to satisfy logical conditions. The strictly formal 
character of such propositions (that is, their complete satisfaction 
of logical demands) is found when the proposition is so fully 
grounded that "only" is a proper qualifier. When the proposition 
is "Only if . . . then. . . ." the proposition is seen to be strictly 
relational. 

This part of the discussion may be concluded by reverting to 
the distinction between contingent conditional and universal (nec- 
essary) hypothetical propositions. Take the proposition "If A 
is to the right of B and B to the right of C and C to the right 
of D, then D is to the left of A." If A, B, C and D are singulars, 
the proposition may be invalid. It is invalid, for example, if A, 
B, C and D are persons or chairs placed around a table. If, how- 
ever, the proposition is understood to mean "Given a straight 
linear arrangement, then the relations are such that anything 
symbolized by D is to the left of whatever is symbolized by A," 
the proposition is in effect a definition of a specified form of space 
relationship and as such is necessary. A, B, C, D now stand not 
for singulars but for abstract characters. 



The special import for logical theory of the present chapter 
is that the various forms of propositions discussed are shown to 
mark stages of progress in the conduct of inquiry. Current theory 
is given to taking the various forms of propositions as given ready- 
made, so that all theory has to do is to fix the appropriate labels 



310 PROPOSITIONS AND TERMS 

on them; particular, general, hypothetical, etc. When they are 
considered functionally, as they have been considered in this 
chapter, (and throughout this work) it clearly appears that par- 
ticular propositions function as instruments for determining the 
problem involved in an indeterminate situation, while the other 
forms listed represent stages in attainment of the logical means for 
solution of the problem. Only if propositions are related to each 
other as phases in the divisions of labor in the conduct of inquiry, 
can they be members of a coherent logical system. When their 
distinctive roles in the institution of final judgment is omitted 
from theoretical interpretation, it just happens that there appear 
to be a number of independent isolated propositional forms. A 
final point is that while the findings of this chapter regarding the 
relational character of all propositions were not developed in 
order to support the doctrine that all propositional forms are 
instrumental to judgment (which alone has subject-predicate 
form), nevertheless the findings are just what would be anticipated 
on the ground of the general theory advanced regarding proposi- 
tions and judgment. 



CHAPTER XVI 

PROPOSITIONS ORDERED IN SETS AND SERIES 



Inquiry is progressive and cumulative. Propositions are the 
instruments by which provisional conclusions of preparatory 
inquiries are summed up, recorded and retained for subse- 
quent uses. In this way they function as effective means, material 
and procedural, in the conduct of inquiry, till the latter institutes 
subject-matter so unified in significance as to be warrantably 
assemble. It follows (1) that there is no such thing as an isolated 
proposition; or, positively stated, that propositions stand in ordered 
relations to one another; and (2) that there are two main types 
of such order, one referring to the factual or existential material 
which determines the final subject of judgment, the other refer- 
ring to the ideational material, the conceptual meanings, which 
determine the predicate of final judgment. In the words of ordi- 
nary use, there are the propositions having the relation which 
constitutes inference, and the propositions having the serial rela- 
tion which constitutes reasoning or discourse. 

The following discussion is concerned, in respect to both types, 
with the logical order of propositions rather than with the tem- 
poral order of propositions in carrying on a given inquiry. In an 
inquiry of any high degree of difficulty many propositions are 
entertained during its course only to be discarded or modified in 
subsequent inquiry. For they are not propositions which sub- 
stantiate the final conclusion even though in a given investigation 
an inquirer would not have reached that conclusion unless he 
had at one time entertained them. The order with which we are 
concerned is of the sort that can be instituted only after an inquirer 
has reached a valid conclusion and surveys the grounds upon which 
it is taken to be justified. The propositions in question are such, 
in other words, as are usually termed premises of a conclusion, 

311 



3n PROPOSITIONS AND TERMS 

subject to the condition that there is no fixed limit to their number. 
This negative proviso is made because the theory of the syllogism 
reduces premises to two, called the major and minor. It will be 
shown later that the conception of but two premises, one universal 
and the other singular or generic, represents the logical structure 
of judgment as a union (copulation) of propositions of predicate 
and subject contents. The doctrine of a duality of premises thus 
provides an analysis of the logical conditions to be satisfied by a 
conclusion, rather than a statement of the premises upon which a 
conclusion actually rests. There is, I repeat, no fixed limitation 
upon the number of premises involved in substantiation of a con- 
clusion. 

1. Dyadic and Polyadic Propositions. If no proposition is a 
proposition in isolation, it follows that the related terms of a given 
proposition are ultimately determined by reference to the related 
terms of other propositions. This consideration applies to the 
number of terms in a given proposition as well as to its contents. 
Recent logical theory has paid much attention to the number of 
terms, distinguishing dyadic propositions, such as "Justice is a 
virtue"; triadic propositions, such as "The point M is the middle 
point between A and 5"; tetradic propositions, such as "European 
nations owe the United States N dollars on account of war loans"; 
etc. Current theory, however, tends to take propositions as com- 
plete in isolation; hence, the current classification is made on 
linguistic rather than logical grounds. From a logical point of 
view, there are but two divisions, dyadic and polyadic. Proposi- 
tions of predicate contents, or universal propositions, have but two 
terms, those of a definition and hypothesis. Propositions about 
factual data which serve as subject-content of judgment are, on 
the other hand, polyadic. Linguistically, there may be only two 
terms. But logically any existence has to be determined with 
respect to date and place. For example, "This is further away 
than that," "James is taller than John," express a relation between 
two-terms as far as words are concerned. But these propositions 
are not necessarily valid but hold of conditions at a particular time 
and locality. The first proposition, for example, obviously means 
further away from the speaker, hearer, or some specified object, 
thus involving a third term. Something of the same sort holds of 



SERIES AND SETS OF PROPOSITIONS 313 

the proposition "A is the husband of B." A date is postulated if 
not expressed, since "is" here has a temporal present tense, not an 
intrinsic logical relation. Any proposition having direct existential 
reference applies to conditions or circumstances. "This is red" 
not always and necessarily, but under specifiable conditions. 
"Socrates is mortal" is not two-termed, because it means Socrates 
is (was) a human being living at some specific time and place, 
who died under specific temporal-spatial circumstances. How- 
ever, there is no need to multiply instances. 

On the other hand, "Man is mortal," is strictly dyadic, when it 
means "If anything is human, then it is mortal," for both terms 
are abstract and the relation affirmed is of abstract nonexistential 
character. The proposition states a relation between conceptual 
contents. The Newtonian formula for gravitation is equally two- 
termed, for it expresses a universal if-then relation between being 
material and being reciprocally "attracted" in a specified way. 
Regarding propositions of predicate contents, it is also needless to 
multiply examples. For they are (1) independent of space-time 
reference, and (2) state a necessary relation between antecedent 
and consequent. No matter how linguistically complex the for- 
mulation may be, no matter how many clauses and phrases are 
involved, the clauses and phrases belong to one or another of the 
two characters that are affirmed to be intrinsically related together. 
A mathematical equation or statement of a mathematical function 
may contain many symbols but they all fall on one side or the 
other of the function which is formulated. 

2. Equivalence of Propositions. So far the discussion has dealt 
with logical properties belonging to both of the main types of 
propositional forms. I come now to a character which belongs 
only to propositions of conceptual or predicational contents, a 
character which marks them off from matter-of-fact propositions. 
When a problematic situation is present, some meaning is sug- 
gested as a possible mode of solution. Unless this meaning is 
formulated propositionally, it is at once accepted and inquiry 
ceases. The conclusion reached is then premature and un- 
grounded. But the meaning suggested is also a member of some 
constellation of meanings. Hence, it is not enough to formulate 
it in a separate proposition. The meaning has to be developed 



314 PROPOSITIONS AND TERMS ^ 

in terms of a set of other propositions which formulate other mean- 
ings that are also members of the system to which it belongs. 
In a word there is reasoning, argument, or ratiocination: Dis- 
course. Furthermore, the development of related propositions in 
discourse has direction. For it is regulated by the nature of the 
problem in which a meaning is to function as a manner or method 
of solution. Apart from reference to the use or application to 
be made of the meaning, a given proposition can be related to 
other propositions in the system of meanings to which it belongs 
in an indefinite or indeterminate variety of ways. But in any 
given discourse a meaning, propositionally formulated, is developed 
in that specially related series of propositions which have direction 
towards a proposition applicable in the stated conditions of the 
special problem in hand. Direction is such an obvious property 
of all reasoning and relevant discourse that it would be superfluous 
to note explicitly its presence were it not for its bearing upon the 
logical problem under discussion. 

There are two logical conditions which ordered discourse must 
satisfy. The order of propositions must be rigorous and produc- 
tive — a proposition in which "and" has other than enumerative 
force. The order must be productively rigorous and rigorously 
productive. To say that the order must be rigorous is to say 
that each proposition following from the initial one — "initial" 
in a logical but not temporal sense — must be equivalent in logical 
force to that which preceded it; otherwise it follows after but 
not from. The phrase "in logical force" is emphasized because of 
the equivocal meaning attaching to "tautology" in current logical 
theory. The principle of equivalence is not identical with that 
of tautology unless tautology is given a special meaning — a mean- 
ing which does not preclude but rather satisfies the condition of 
productivity. The conceptions or meanings found in subsequent 
propositions in the order of rational discourse are identical with 
those of antecedent propositions in operational force not in content 
and hence lead rigorously to meanings having another content. 
It is this difference of content that constitutes productivity in 
reasoning. The principle of direction is applicable at this point. 
What is demanded is a formulation of the meaning set forth in 
abstract universal form in the initial proposition such that it 



SERIES AND SETS OF PROPOSITIONS 315 

operatively leads to a proposition existentially applicable in a way 
in which the content of the initial proposition was not applicable. 
Satisfaction of the condition of rigor does not mean tautology in 
the sense that the dyadic terms of the initial abstract universal 
propositions are repeated in linguistic forms that are synonymous. 
For example, in the proposition "An electric current is equal to 
the potential difference divided by the resistance," the term poten- 
tial divided by resistance does not have the same immediate denota- 
tive or existential reference as "electric current." But the 
equivalence of conceptual contents affirmed in the proposition 
enables a subsequent proposition to be stated about something 
which is in turn equivalent to "potential divided by resistance," 
and so on. The term current does not appear in the proposition 
following it, and potential divided by resistance is replaced in the 
proposition which follows it by a relation between it and some- 
thing else which is its equivalent. And so on until a proposition 
appears in a form operationally applicable in an experimental 
situation which yields material indispensable to the solution of the 
problem in hand, or at least to an improved statement of what 
the problem is. The conceptions of currents, of differences in 
the conductivity and resistance of metals, and of differences in 
the strength of currents, are ideas that must have arisen at a com- 
paratively early time. They certainly arose long before the law 
mentioned above was arrived at. The statement of a determinate 
ratio or relation between previously independent conceptions was 
in effect a new way of conceiving all of them. It was, moreover, 
a way of conceiving them which enabled generalized relations to 
be followed out in a rigorous way. Equivalence is thus capacity 
for substitution of meanings in the series of propositions which 
constitute reasoning. There is, therefore, nothing miraculous in 
the fact that "deduction" yields propositions having contents 
which are other than that of those from which they were derived. 
For the propositions employed in demonstrative discourse or de- 
duction are themselves framed with express reference to per- 
formance of this function. The trick of science, so to speak, does 
not consist in its dialectic or reasoning aspect, though here, too, 
sagacity is demanded save in all cases so familiar that calculation 
becomes mechanical. The chief difficulty and the chief insight 



316 PROPOSITIONS AND TERMS 

in overcoming the difficulty consists in the formulation of related 
meanings such that equivalent propositions are progressively and 
productively (and yet rigorously) substitutable in development 
of propositions in series. 

The conjugate relation already noted between propositions of 
abstract or ideational contents and of matter-of-fact propositions 
arises from the fact that the subject-matter of a hypothesis is first 
suggested by the original problem and is then tested and revised 
on the ground of its consequences. The guiding criterion is the 
power of these consequences to promote solution of the problem 
in hand. The requirement set by continuity of inquiry is satisfied 
to the degree in which the range of substitutibility is enlarged. 
When equivalences are established only within a limited frame of 
existential reference, say, of problems of heat, or of mechanical 
changes (changes described in terms of motions spatially and 
temporally formulated) in isolation from each other, the domain 
of productive reasoning is in so far restricted, even though it is 
much wider than that of common sense. When hypotheses are 
formed so comprehensively in scope that they are applicable to 
the facts of temperature, electricity, light and mechanical motion, 
the degree of freedom enjoyed in the institution of equivalences, 
and therefore in reasoning, is enormously increased. Special "sys- 
tems" then become members of a comprehensive system. Because 
of the conjugate relation of propositions of this form to matter-of- 
fact observational propositions the range of inference is corre- 
spondingly widened. 

What has been said is directly applicable to the conception of 
indemonstrable propositions as the original ground of all rational 
demonstration. It is certainly true that in every instance of reason- 
ing there is an initial proposition, not derived or "deduced" in 
that particular discourse, since to say that it is initial is the same as 
saying that it does not follow from predecessors. But (1) there 
is nothing inconsistent in its being initial in that set of propositions 
with its being a successor or final proposition in some other series. 
The continuity of inquiry involves, on the contrary, that conclu- 
sions in one problem or set of problems become starting points of 
discourse in dealing with new problems. The very conception 
of a system (alluded to in the previous paragraph) and of a system 



SERIES AND SETS OF PROPOSITIONS 317 

of sub-systems means just this sort of prepared possibilities of 
cross-reference, reciprocal borrowing and lending between differ- 
ent instances of reasoning. (2) The initial proposition is a hypo- 
thetical universal taken and used for the sake of what it will lead 
to. It is tested and retested as a hypothesis by its productive 
capacity in the institution of other universal propositions, while 
it is finally tested by the existential consequences of its application 
to matter-of-fact conditions. Its proof lies in these consequences, 
as the proof of a pudding is in the eating. When propositions 
are produced which contradict either an initial or a successor 
proposition, a new problem is set. In such cases it is usually found 
that the predecessor proposition in the series can be so modified as 
to meet the requirements of rigor only by meanings arising from 
new experimental operations. 

It follows from what has been said that rigor-productivity are 
logical conditions which universal propositions in series have to 
satisfy; they are not, primarily, properties of any given series. They 
are rather limiting ideals which state the intent of any proposition 
of predicative content. They are not premises — save in logical 
theory itself — but are leading principles. The deliberate attempt 
to satisfy the formal conditions prescribed by rigor-productivity 
in abstraction from material subject-matter constitutes mathemat- 
ics. This statement does not mean there is some domain marked 
off in advance to which mathematical propositions and reasoning 
apply. The meaning is the contrary: the regulated attempt to 
satisfy these conditions is mathematics. 1 

3. Independence and Cumulative force in Alatter-of~Fact Prop- 
ositions: Propositions which determine the subject-content of final 
judgment are ordered by a different principle. One does not 
follow from another in the sense of being implied, or directly 
substitutable in logical force. On the contrary, the force of each 
such proposition is measured, first, by its having an independent 
subject-matter which is determined by an independent experi- 
mental operation; and, secondly, by its conjunction with other 
propositions about independent subject-matters by which cumu- 
lative convergence may be reached. Existential propositions are 

1 There is much in common between the account of the text and James 7 
exposition of skipped intermediaries. See his Psychology, Vol. II, 645-51. 



318 PROPOSITIONS AND TERMS _^ 

ordered because they are controlled by reference to the same 
problematic situation, and in so far as they promote its resolution, 
However, they do not form a series, but a set. In reasoning, serial 
propositions may be likened to the arrangement of the rungs of a 
ladder. Propositions about factual data, which serve to provide 
the evidence which grounds inference, are more like lines that 
intersect one another and which, in intersecting, describe a con- 
figurate area. In series of the ladder type sequential order is 
essential. With respect to propositions which determine evidential 
properties, ordinal position is not important. The logical order 
of the series (as distinct from the historical order of operations 
by which relevant and weighty data are secured) is constituted by 
the relations of inclusion (affirmation) and exclusion (negation, 
elimination) which define comparison. Operations of experimental 
observation (1) narrow the field of relevant evidential material 
and (2) effect intersections that converge towards a unified signify- 
ing force and hence to a unified conclusion. 

For example, a physician in his diagnosis executes independent 
operations which yield a variety of independent data, regarding 
temperature, heart-beat, respiration, kidney excretions, state of the 
blood, metabolism, history of patient, perhaps his heredity, etc. 
These independent explorations are carried on as long as the 
significance of the data obtained by them remains obscure — that 
is, as long as they cumulatively fail to point in a determinate 
direction. What is usually called correlation of data is a matter 
of convergence in significance, of cumulative evidential force. 
Taken separately, such propositions have indicative force as to 
the nature of the problem and its possible solution. As they con- 
verge, they have probative force. Indicative force, when it is 
determined by elimination of alternative possible modes of solution, 
becomes signifying force. The conjugate connection of factual 
and conceptual propositions has the effect of enabling the con- 
ceptions already in hand (a matter depending upon the state of 
theory and the systematization of conceptions at the time), to 
determine the operations by means of which new, independent 
explorations are made and their results interpreted. 

It is a familiar logical principle that affirmation of the consequent 
does not warrant complete affirmation of the antecedent. Denial of 



SERIES AND SETS OF PROPOSITIONS 319 

the consequent grounds, however, denial of the antecedent. When, 
therefore, operations yield data which contradict a deduced con- 
sequence, elimination of one alternative possibility is effected. 
Recurrent agreement of the indicative force of data, provided they 
are secured by independent experimental operations, gives cumula- 
tive weight to the affirmation of an antecedent whenever we can 
affirm the consequent. The affirmation of any given hypothesis 
proceeds in this way. But the possibility of the fallacy of affirm- 
ing the antecedent still remains. Elimination of other possibilities 
progressively reduces the likelihood of fallacious inference. But 
there is never assurance that all alternative possibilities have been 
exhausted, because there is no assurance that the disjunction of 
alternatives is exhaustive. Hence probability is the mark of every 
proposition effected by inference from the set of matter-of-fact 
propositions, just as necessity — or rigor — is the mark of the non- 
existential proposition instituted through demonstrative discourse. 
Hence, exhaustiveness is not a property of any actual disjunctive 
set, but is a logical condition to be satisfied. 

Comparison, as we saw, is a mode of measurement. It is deter- 
minate in the degree that measurement results in numerical state- 
ments. Measurement is possible because observed phenomena are 
enduring and extensive. The techniques of measurement translate 
endurance and spread, which are purely qualitative in immediate 
experience, into spatial-temporal relations, numerically formulated. 
It is of course a basic property of numbers that relations of equiva- 
lence can be instituted between them. In the actual practice of 
science, it is the agreement of numerical measurements of observed 
phenomena with those theoretically deduced from a hypothetical 
proposition which has the maximum of probative force. Qualita- 
tive endurances and extensive spreads run into one another. The 
existential conditions of any existence are indefinitely circum- 
stantial. Otherwise stated, there can be no absolute guarantee 
that the selection of the phenomena which are numerically deter- 
mined effects only those discriminations that are necessary to 
yield probative data. Hence precision of measurement and agree- 
ment of its results with deduced conclusions, is, as far as final 
evidential significance is concerned, subject to a condition which 
cannot be completely or absolutely controlled: namely, the validity 



320 PROPOSITIONS AND TERMS 



of the original selective discrimination of the subject-matter of 
observation. 2 

Even were it possible to find a piece of gold that is pure gold, 
that is gold and nothing but gold, it could not be completely 
isolated from interactive connection with an indefinite variety of 
circumstantial conditions. A high degree of control of conditions 
is effected by the scientific techniques now available. But there al- 
ways remains the theoretical possibility that some conditions which 
affect the observed phenomenon have not been brought under con- 
trol. The postulate of a closed existential system is thus a limiting 
ideal for experimental inquiry. It is a logical ideal which points the 
direction in which inquiry must move but which cannot be com- 
pletely attained. Hence, the statistical character of all factual 
generalizations is not a matter of defective techniques (although 
defective technique represents a failure to observe the conditions 
imposed by the logical condition to be satisfied), but is a matter 
of the intrinsic nature of the existential material dealt with. 

The assumption that qualities literally recur (or are universals) 
is a fallacy (as was earlier noted) arising from confusing the con- 
stancy of evidential function — a product of continued inquiry — 
with immediate existential qualities. No quality as such occurs 
twice. What recurs is the constancy of the evidential force of 
existences which, as occurrences, are unique. When it is held 
that there is strict or implicatory necessity in the series of proposi- 
tions "John is taller than James, James than William, and, there- 
fore, John is taller than William"; it is overlooked that tall is a 
quality subject to change, by change in conditions. Practically 
speaking, no one would doubt that in some cases the conclusion 
is valid. But if we take the case of three things of approximately 
the same length, it is obvious that during the operation of measure- 
ment one of them may change its quality of length in spite of 
all efforts to maintain constant conditions. Hence, in theory the 
inference is of a certain order of probability, not necessary. The 
proposition "If A is longer than B, and if B is longer than C, then 
A is longer than C" is necessary when and since its contents are 

2 This fact agrees with the indefinitely extensive character of the perceptual 
field, and is in so far a confirmation of what was said earlier. See, ante, pp. 
66-7. 



SERIES AND SETS OF PROPOSITIONS 321 

abstract, not when A, B and C are singulars. The proposition 
is necessary as a definition. But that John, James and William 
as existences actually satisfy the conditions imposed by the defi- 
nition does not follow from the definition. The conception 
that propositions about the existences in question, have the im- 
plicatory "transitivity" characteristic of the terms of the univer- 
sal proposition is a fallacy depending upon doctrinal confusion of 
the logical properties of non-existential and existential propositions. 
It requires independent experimental operations to determine 
whether connections between existences satisfy the conditions laid 
down in a universal hypothetical proposition. In some cases, there 
is, as was just said, no practical difficulty in the way of perform- 
ing the required operations. But the validity of the resulting con- 
clusion rests wholly upon involvements among observed facts, not 
upon a necessary implicatory relation. The latter prescribes the 
operation to be performed, but is not identical with the circum- 
stantial connection of existences with one another. 

4. Transposition of Terms. Every logical text states the rules 
according to which the terms of a proposition may be transposed 
without affecting the logical force of a proposition. When a 
sentence is taken in isolation and not as a member of a serial ar- 
rangement in reasoning or inference such changes are merely 
grammatical. But every proposition in the logical sense of the 
term is a member of an ordered set or series of propositions. 
Every such set and series is framed w T ith reference to the function 
to be served by either its final member or by cumulative con- 
vergence in effecting final judgment. Certain arrangements of 
terms within a. proposition are more effective than are other ar- 
rangements in carrying forward the needed progression to a termi- 
nal proposition or else in giving it the form that best indicates its 
force in the set of independent propositions. This accounts for 
the logical importance of the changes in position called conver- 
sion, obversion, obverted converse, inversion, contraposition and 
obverted converse. It follows that no initial existential proposition 
can be converted simply. No one would suppose that the logical 
force of "All crows are black" is identical with that of "Any 
black thing is a crow." The legitimate transposition is "A black 
thing may be a crow." Stated in this form, the proposition has a 



322 PROPOSITIONS AND TERMS 

new functional force. It indicates an investigation to be under- 
taken with a view to finding out whether black in this case is 0r 
is not conjoined with other traits which describe the kind crom, 
Blackness is in some actual cases a suggestion worth developing! 
Such propositions as "Iron is a metal" are ambiguous apart from 
context. The more obvious interpretation is that it refers to 
a relation of kinds. It might, however, mean that "If anything 
has the characters which define being iron, then it has the char- 
acters which define being metallic." In the latter interpretation 
it is, as we have said, universal In either case, convertibility de- 
pends upon the completeness of terms related in the proposition in 
question. As the proposition cited stands, the term metal is wider 
than the term iron, so that simple conversion is not possible. Con- 
version would then again give the transposed form the force of 
may, and so be a step in further observational investigations. But 
if the relations of sub-kinds with the kind metal have their differ- 
ential traits already determined, as of iron with respect to tin, 
zinc, copper, etc., then the proposition is convertible simply, 
though with an order of probability dependent upon the exhaus- 
tiveness of the disjunction involved. That is, "metal" limited by 
specified differential traits is iron just as iron is a metal. 3 

The exact relation of what is called immediate inference to trans- 
position of terms is a somewhat ambiguous matter. In some cases 
they are synonymous. Such is not the case in immediate inference 
by added determinants and by subimplication. In any significant 
instances of the two latter processes, inference is not, however, 
immediate. The ordinary textbook illustrations of "added deter- 
minants" are trivial because their subject-matter is familiar and 
standardized. The significant cases are those in which determi- 
nants are added because a proposition as it stands is too broad (or 
too general in the sense in which general means vague). In this 
case, an independent proposition or propositions is (are) required 
in order to determine whether the limiting determinant has an 
equivalent force when applied to both terms of the vague propo- 
sition. In such cases there is mediation. An example of sub- 
implication is the following: "The sum of three angles of a 
Euclidean triangle is two right angles." Hence "The sum of the 

3 CF. ante, pp. 308-9. 



SERIES AND SETS OF PROPOSITIONS 323 

three angles of a scalene triangle is two right angles." Here the 
second form does follow by implication; it is called ^implication 
simply because the particular inquiry in hand happens to call for 
a specific limitation or narrowing in the movement toward a 
terminal proposition. When however, logical texts state that the 
relation of a verifying case, expressed in an existential proposition, 
to a universal proposition (theoretical law or hypothetical for- 
mula) is that of subimplication, there is a plain fallacy involved. 
No non-existential proposition implies an existential one. 

5. The Syllogism. A syllogism is an analysis of final judgment 
into its logically constituent propositional conditions. As has been 
pointed out, these logical constituents are (1) a proposition re- 
garding matters-of-fact and, (2) a proposition regarding a relation 
of abstract characters, or conceptual contents. The formulation 
of the matter-of-fact ground constitutes the minor premise; that 
of ideational and hypothetic content constitutes the major prem- 
ise. The syllogism is thus a generalized formula for logical 
conditions that must be satisfied if final judgment is to be grounded. 
It is, so to speak, a warning that in order to warrant a final judg- 
ment a conjugate connection between observed data and a con- 
ception, defined in a universal if-then form, must be instituted. 
Supposing the conclusion has been reached that a bat is a bird — 
the explicit minor would be "The bat has wings." In order to 
ground the conclusion "A bat is a bird" it would be necessary to 
lay down a general proposition to the effect that "all winged 
creatures are avian" where all has the force of a relation of char- 
acters. To warrant the conclusion completely, it would be neces- 
sary to establish the proposition "Birds and only birds are winged." 
Statement of the predicate-content in a proposition as a major 
premise is a necessary check upon drawing a conclusion. It func- 
tions as a directive for observational inquiries whose consequences 
tend in the direction of an inclusive-exclusive proposition. 

The above account does not agree with the traditional theory. 
For the latter theory identifies, as a rule, the syllogistic with the 
ratiocinative or deductive form. It thus (1) leaves no room for 
an existential proposition and (2) makes a fetich of the idea that 
there can be only two "premises" in a ratiocinative series, an idea 
negated by every form of mathematical reasoning. The idea that 



324 PROPOSITIONS AND TERMS 

a minor existential proposition can be deduced from a universal 
proposition represents a confusion which has been repeatedly com- 
mented upon. No matter whether the minor proposition is singu- 
lar (one of a kind) or is generic (a relation of kinds), it has to be 
instituted by independent operations of experimental observation. 
When the syllogism is of the A A A form, the proposition which 
is the minor premise is a generic but not a universal proposition 
since it is existential in reference. In any actual case it is therefore 
of a certain order of probability,. i.e., an / proposition. This fact 
shows that the syllogism of the form of Barbara cannot, when the 
minor premise has existential reference, be regarded as setting 
forth properties possessed by any actual inference. When treated, 
however, as a formula setting forth the logical conditions to be 
ideally satisfied by an inferential conclusion, the case is different. 
The general character of the minor proposition is then a way 
of stating that, ideally, or in strict theory, there should be a strictly 
conjugate relationship between the definition set forth in the 
major and the matters-of-fact constituting the minor premise. 
The syllogism, thus construed, means that a conclusion is logically 
warranted, and is only so warranted, when the operations involved 
in discourse and in experimental observation of existences, con- 
verge to yield a completely resolved determinate situation. 

Such an interpretation gives the syllogism logical importance 
and indispensability. It involves, however, a marked revision of 
the Aristotelian theory of the syllogism. For in Aristotle's logic, 
the major premise, or definition, was the statement of an essence 
which ontologically determines a species, while the minor premise 
affirmed that some species fell existentially within that wider 
species — or else was an actualization of the logical potentiality 
represented by a genus. Here, as in other cases previously men- 
tioned, the bare form has been retained in traditional logic after 
its ontological ground (of fixed species and essences) has been 
repudiated. Hence it was exposed to Mill's criticism. However, 
Mill retained the logical error of the traditional theory although 
in a reversed direction. The traditional theory holds that major 
and minor are of the same logical form, failing to recognize that 
one is non-existential and the other existential; and that, therefore, 
they have to be instituted by operations which are as different as 



SERIES AND SETS OF PROPOSITIONS 325 

are observation and rational discourse. Mill's theory makes the 
same error, save that now both major and minor are treated as 
existential, so that instead of assimilating the form of the minor 
to that of the major (as the traditional theory does), Mill assimi- 
lated the form of the major to that of the minor. That is to say, 
Mill holds that the major or general proposition is a summary 
memorandum of an indefinite number of particular existential 
propositions. 

It is not correct to say, as is sometimes done, that Mill held that 
the syllogism involves a petitio principiL What he affirmed was 
that if the major be taken to prove the conclusion, then the con- 
clusion of the syllogism begs the question, since in that case the 
latter is already included in the major premise. He says the major 
provides the formula "according to which but not by which the 
conclusion is drawn." It is, he says, "an assertion of the existence 
of evidence sufficient to prove any conclusion of a given descrip- 
tion." 4 Proof on this view is provided exclusively by the various 
particular observed cases which the general or major premise sums 
up. Not an iota to probative force is added, he says, by the gen- 
eral as such. That he assimilates the form of the major to that 
of the minor is not only involved in his whole treatment but is 
explicitly affirmed, as when he says "the mortality of John, 
Thomas, and others, is, after all, the whole evidence we have for 
the mortality of the Duke of Wellington" — or any other person 
who has not as yet died. 5 

Mill's interpretation would be sound if evidential force were a 
matter of ^//-evidence; that is, if no principle or universal were 
required to decide what is evidence and what is not and how 
weighty and relevant are specific data in any given case. As it is, 
he begs the question by assuming that particulars as such are al- 
ready equipped with adequate evidential capacity. In the language 
we have already used, particulars suggest a certain idea (which is 
general) but they do not validly signify, much less prove it. The 
whole problem of inquiry, upon the observational side, is to de- 
termine what observed conditions are evidential data or are "the 
facts of the case." What has already been determined to be evi- 

* Logic, Book II, Chap. 3, Sec. IV and Sec. VI. 
*Md. } Sec. in. 



326 PROPOSITIONS AND TERMS 

dence has probative force; that statement is a mere truism, since 
evidence and probative force are synonyms. What Mill fails 
to see is that observations, in order to yield evidential material, 
have to be directed by ideas and that these ideas have to be made 
explicit — formulated in propositions, and that these propositions 
are of the if-then universal form. What Mill has in mind by "suf- 
ficiency" of evidence is simply the number of particulars at hand, 
not the principle by which the evidential force of any particular 
is determined. 

Mill's sense for fact leads him, however, into a deviation from— 
indeed, into a contradiction of — his official doctrine. This devia- 
tion approximates, if it is not identical with, the interpretation of 
the syllogistic form which has been given. The official doctrine 
is that the general proposition is "an aggregate of particular 
truths." But he also states that "Truth can only be successfully 
pursued by drawing inferences from experiences which, if 'war- 
rantable at all, admit of being generalized, and which, to test their 
tuarrantableness, require to be exhibited in generalized form." 6 
Again, instead of treating the general proposition as a bundle of 
particulars as particulars, he says at times that it states the "co- 
existence of attributes" — that is of characters, and expressly adds 
that "coexistence" is not to be understood in a temporal sense but 
in the sense of the property "of both being jointly attributes." 7 

Mill also states that the general or major is reached by induc- 
tion, and while his theory of induction is confused, it assuredly 
involves operations of analyzing the material of gross observations 
together with operations of elimination, and of determination of 
agreement in evidential function, while he is obliged to admit the 
importance of hypotheses although he gives them only a "sub- 
sidiary" place. 

Traditional theory affords another instance of the ambiguity 
of ally since it rests upon taking all in both an existential and non- 
existential sense. Supposing it is said "All whales are mammals: 
all mammals are warm-blooded, therefore all whales are warm- 
blooded " If the example is an exemplification of analysis of a 
logically grounded judgment, then the major is an if-then uni- 

*Ibid. 9 Sec. IX; italics not in original text. 
1 Ibid., Sec. IV, and footnote. 



SERIES AND SETS OF PROPOSITIONS 327 

versal proposition, affirming that there is a necessary relation be- 
tween being mammalian and being cetacean such that a negation 
of the relation involves contradiction. The proposition, if valid 
at all, is valid even if whales have ceased to exist. As an opera- 
tional proposition, it directs observation to ascertain whether in 
the case of existential singulars the traits of suckling young, pro- 
ducing them alive, etc., are found in conjunction with one another. 
On the other hand, all in the proposition "All whales are mam- 
mals" may mean that so far as singular whales have been observed, 
they have been found to be, without exception, mammalian. This 
proposition means "Whales may be mammals" and indicates that 
possibility so strongly as to instigate search for the reason why the 
traits are conjoined — that is, it instigates search for a relation of 
characters which will institute an if-then proposition. Until some 
reason is instituted capable of this formulation final judgment is 
not reached. Inquiry is still in the propositional stage in which 
singulars are observed and hypotheses are formed and tried out. 
Upon examination it will be found that the difficulties which 
have been alleged to inhere in the syllogistic form arise from 
identifying it with properties possessed by reasoning or of infer- 
ence taken in separation from each other. They vanish when it 
is seen that it does not purport to be the form of either inference 
or rational discourse. It is the form of the conjugate connection 
of the factual and conceptual subject-matters of judgment, stated 
in such a way as to indicate the conceptual and observational con- 
ditions to be fulfilled if judgment is to be adequately grounded. 
Interpreted in this way, the "utility" of the syllogistic form 
resides in the fact that it serves as a check in the case of specific 
judgments, holding up the logical conditions that are to be satisfied. 
It represents a limiting ideal Even though no actual judgment 
really satisfies the ideal conditions, a perception of failure to do so 
occasions and directs further inquiry upon both the observational 
and the conceptual sides. It promotes and supports the continuum 
of inquiry. 



CHAPTER XVII 

FORMAL FUNCTIONS AND CANONS 



A ccording to the doctrine developed in previous chapters, 
/_\ every term (meaning) is what it is in virtue of its mem- 
A )V bership in a proposition (its relation to another term), 
and every proposition in turn is what it is in virtue of its member- 
ship in either the set of ordered propositions that ground inference 
or in the series of propositions that constitute discourse. It fol- 
lows from this position that the logical content and force of 
terms and propositions are ultimately determined by their place 
in the set of propositions found in either inference or discourse. 
Order is thus the fundamental logical category with respect to 
determination of the meaning of terms, directly in propositions and 
indirectly in sets and series of propositions. 

I. FORMAL RELATIONS OF TERMS 

The fundamental rules of logical ordering of terms are known, 
technically, as transitivity, symmetry and correlation, while con- 
nexity is an important instance of their conjunction. Failure of 
terms to satisfy required logical conditions of order constitutes 
them intransitive and asymmetrical, while non-transitive and non- 
symmetrical characterize terms in their status as still indeterminate 
and problematic. The statement as respects intransitivity and 
asymmetry will be justified in later discussion. But it holds 
truistically in the case of 72072-transitivity and non-symmetry,, since 
these relations by definition are of terms which may be either of 
one type or the other and hence are ambiguous in logical form. 

The list, just given, of different types of relations sustained by 
terms to other terms, is one found in all modern logical treatises. 
The usual doctrinal interpretation is, however, quite different 
from that here given. For in current treatment, it is assumed that 

328 



FORMAL FUNCTIONS AND CANONS 329 

terms sustain these relations in and of themselves by the inherent 
nature of their own content. If this assumption is not always 
explicitly stated, it is implicit in failure to interpret terms on the 
ground of their functional force in satisfaction of the logical con- 
ditions of order that are imposed by the demands of valid infer- 
ence and discourse. Stated positively, the doctrinal position 
expounded demands that formal relations of terms be interpreted 
as conditions which terms must satisfy in any inquiry that yields 
warranted conclusions, not as their inherent possession. 

The reason why the relations that have been mentioned are 
usually illustrated by isolated terms is not far to seek. Many 
terms have been so standardized in the course of prior inquiries 
that their relational meaning can now be taken for granted and 
treated as if it belonged to them apart from their status and force 
in the conduct of continuous inquiry. This is strikingly true in 
the case of mathematical terms. It is also true in the case of such 
terms as father of, wife of, spouse of, etc. For their meaning is 
now settled by their place in some (contextual) ordered system 
of conceptions, which is so familiar that it is first taken for granted 
and then so completely ignored as to be virtually denied. There 
are said to be Australian tribes that do not have the conception 
of begetting, and in which therefore the conception "father of" 
can hardly be said to exist. There are many tribes in which 
"father of" expresses the relation called in our system "uncle of." 
Such facts indicate the relativity of these relative terms to a system 
of related meanings, biological or legal or both. 

Before dealing severally with the different forms of relation, 
it is advisable, in the interest of avoiding doctrinal confusion, to 
recur to the basic logical distinction between terms having re- 
spectively existential and non-existential import. For relation and 
related are highly equivocal terms. There are terms that are 
relative but whose meaning is not exhausted in the relation speci- 
fied. "Father of" is clearly a relative term; its meaning depends 
upon connection with another term, "offspring of." The same 
thing is true of terms like short, small, rich, near, next, between, 
etc. Indeed, it is true of all existential terms that have been pre- 
pared so as to function in inferential operations. But the singular 
who is father of has traits in excess of being a father; traits, more- 



330 PROPOSITIONS AND TERMS 

over, that must exist independently of and antecedent to the "rela- 
tion" in question. Any one who is of the kind "fathers" must, for 
example, possess the independent characteristics of being an ani- 
mal, a male, having sexual potency, ttc. Similarly, that which is 
short, small, near, etc., has an existence independent of the content 
expressed in these relative terms. Abstract terms, however, like 
fatherhood, length, magnitude, nearness, nextness, are exhaustively 
and exclusively relational. This exhaustiveness is what constitutes 
them abstract and universal terms. The same thing holds of words 
that are pure connectives, like conjunctions, prepositions, and in 
general, what Chinese grammarians have aptly called "empty 
words." It holds strikingly of all mathematical terms as such. 
In order to avoid the latent confusion present in the words "rela- 
tive" and "related," the words "relatives" will here be reserved 
for existential terms that have a multitude of connections with a 
multitude of things other than that specified in the given related 
term — as a father is also, say, a citizen, a Republican, a Methodist, 
a farmer, etc., all of these words expressing relations which are 
logically independent of the relation designated by "father." The 
term "relational" on the other hand, will be used to designate 
abstract terms whose meaning is exhaustively contained in the 
terms. 1 

1. Transitivity and Intransitivity. In order that inference may 
be grounded from one set of traits to another or from one kind 
to another, and in order that propositions may be so ordered in 
discourse that subsequent ones follow necessarily from antecedent 
ones, the terms involved must be ordered in that relation to one 
another known as transitivity. Take such terms as "older than" 
(greater, brighter, etc.), or any property expressed linguistically 
by a comparative word. If A is more (or less) in any designated 
trait than B, and B sustains this same relation to C, and C to D, and 
so on, then A sustains it to the last term in the series, whatever that 
may be. The terms satisfy the condition of transitivity. Inter- 
mediaries may be skipped whenever terms have been constituted 
to satisfy this form of order* The relation is found also in terms 
that have to one another the serial order designated by after or 
before, in both the spatial and temporal sense of these words. 

1 The distinction is identical with that between involvement and implication. 



FORMAL FUNCTIONS AND C AXONS 331 

The importance of serial orders prepared in advance in the case of 
relations designated by comparative terms and terms expressing 
spatial and temporal contiguities, together with the need of a 
principle that functions as a method or rule of so determining 
them, may be illustrated as follows: It would be theoretically 
possible to pick out members of a random crowd so as to rank 
them in the order of age from the oldest to the youngest. The 
transitive function expressed in "older than" would then be satis- 
fied. But nothing would come of it. Nothing could be inferred 
as to any other traits of the singulars thus ordered. In similar 
fashion, take a row of books placed haphazardly on a shelf. Each 
book, after the first one, is "after" the one before so that the last 
book on the shelf is after every other one. Nothing, how r ever, 
follows. When, on the other hand, singular persons insured in a 
life insurance company are arranged by yearly intervals in the 
order of older than, something does follow. There is inference to 
probable risks assumed, and hence to the amount of premiums to 
be paid by those occupying different positions in the series. 

Take the case of after in its temporal sense. As I write, the 
sound of a motor car comes after the sound made by a typewriter 
key, and the sound of rustling leaves after that, and then the sound 
of a voice. Hence the last sound comes "after" that of the type- 
writer. The logical import of transitivity is obviously not satis- 
fied by such a succession. It is artificial and trivial. One of the 
most pressing problems of scientific inquiry is to distinguish cases 
in which there is mere succession from those in which there is 
sequence. Repeated observation may determine an order of suc- 
cessions but an inference based upon it will be a case of the fallacy 
of post hoc, ergo propter hoc, unless some principle, stated in a 
universal proposition, gives, as it is operatively applied, a reason for 
the order. Such illustrations provide convincing evidence of the 
logical necessity for interpreting the relation of transitivity as a 
condition to be satisfied in the continuum of inquiry instead of 
being a relational property that just happens to belong to some 
terms. 

The relation of transitivity is also exemplified in terms denoting 
kinds when, and only when, an extensive or inclusive kind has 
been determined with respect to included kinds in an order of 



332 PROPOSITIONS AND TERMS 



progression. To take a simple example: When whales have been 
determined to be mammals and mammals to be vertebrates, there 
is warranted transitivity from whales to vertebrates. This 
transition is logically possible only when the set of conjoiried 
characteristics that describe each kind has been previously in- 
clusively-exclusively determined by the functions of affirmation- 
negation. Scientific natural inquiry is notoriously concerned to 
establish related kinds. This concern is not final, its purpose being 
to institute terms that satisfy the condition of transitivity, so that 
systematic inference is promoted and controlled. 

So far, we have been concerned with transitivity as it affects 
terms, singular or generic, having existential reference. But the 
discussion has also shown that only terms that are serially ordered 
by means of a general principle can actually possess the relation 
in question. This principle is a rule for ordering, and is expressed 
in a universal proposition. This universal proposition must itself 
be in turn a member of a series of propositions in ordered dis- 
course. Mathematical terms are typical examples of non-existential 
terms instituted so as to warrant transitivity in discourse. They 
are strictly relational, not merely relative. The abstract relational 
terms -fatherhood, sonship, unclehood, nephewship, etc., in their 
distinction from the relatives "father-son, uncle-nephew," desig- 
nate relationships which are independent of related existences. 
One cannot infer from the related term father the related terms 
grandson or nephew. The offspring in question may not them- 
selves have offspring, and the fathers in question may not have 
brothers or sisters; and if they have, the persons in question may 
not have sons. The relations are intransitive. But paternity, 
grandfathership, brotherhood, uncleship, cousinship, etc., consti- 
tute a system of relationships such that each is transitively related 
to every other. 

The nature of intransitivity is illustrated in the previous para- 
graph. Terms exemplifying this relation constitute as they stand 
the conditions of a problem. They suggest or indicate the need 
of operations which will transform them into terms that satisfy 
the requirement of transitivity. They indicate, on one side, the 
incompleteness of inquiry in a given case, and, on the other side, 
the operations by which the terms in question may be so ordered 



FORMAL FUNCTIONS AND CANONS 333 

that their meanings will be such as to fall into a determinate 
order. All terms designating particular acts and changes are logi- 
cally intransitive. Take for example, the meanings of A and B as 
related in the proposition CC A killed B " where "killed" stands for 
an act performed by a singular at a particular place and time which 
effects a change in something else. Every particular proposition 
(in the logical sense of "particular") is of this sort. Every such 
proposition expresses a problem or a special condition in the de- 
termination of a problem. 2 

Hence, such terms are intransitive not because of some pecu- 
liarity they possess in and of themselves, but precisely because as 
they stand they are not ordered with reference to determination 
of a spatial or temporal relation, or a relation of kinds, such that 
inference is warranted. When the act of killing is determined in 
connection with a graded series of kinds, as it is in a legal system, 
to be a case of accident, self-defense, or murder in a definite degree, 
it then acquires a meaning satisfying the condition of transitivity. 
Grounded inference is then possible to other previously unob- 
served traits, and to specified existential consequences. This trans- 
formation is effected, as has been previously shown, by ascertaining 
traits which are consequences of modes of interaction and employ- 
ing them, instead of immediate qualities, as the ground of infer- 
ence. For a mode of interaction is general, while a change is not. 
Hence the latter provides no ground for transition, while a kind 
of change which is a specified mode of a more extensive mode of 
interaction has the ordered relation necessary for transitivity. The 
equivalent of this condition in scientific inquiry is the requirement 
that every given change be determined to be a constituent of a 
definite set of correlated changes. 

2. Symmetry and Asymmetry . Terms are relative to each other 
in the sense of symmetry when each one of the related pair bears 
the same relation to the other. "Partners," for example, is a sym- 
metrical relation. If A is a partner of B, then B is a partner of A. 
"Spouse" is a term applied to objects each of which is symmetri- 
cally relative to the other. In other pairs, there exists the relation of 
converse symmetry. The relation of "husband-wife" is itself asym- 
metrical but the terms have the relation of converse symmetry. 

2 See, ante, pp. 201, 220. 



334 PROPOSITIONS AND TERMS 

"Testator-heir" are terms that sustain this relation to each other. 
The relation of converse symmetry exists in all cases of particular 
acts and changes, as in the examples of intransitivity given above. 
The relation is expressed grammatically by the active and passive 
voices of the verb. If A kills B, then B is killed by A. The same 
relation holds in the cases of action and of being acted toward 
(though not upon) linguistically expressed by intransitive verbs. 
The logical import of the relation of symmetry is constituted in its 
conjunction with transitivity. This conjunction is typically ex- 
pressed in the formula: "Things that are equal to the same thing 
are equal to one another." The conjunction of symmetry and 
transitivity constitutes the meanings which validate substitutability 
in inference and discourse. Equality of magnitudes is an obvious 
case of terms that have symmetrical-transitive relativity. 

The scope of the conjunction is not limited to quantities con- 
stituted by operations having existential reference. One who 
measures the floor of a room with reference to determining the 
amount of carpet to be purchased does so in order to institute 
terms having symmetrical transitive relations to each other. Al- 
gebraic equations exemplify terms having this conjunct relation 
in respects other than that of magnitude. Physical functions are 
generalizations which warrant substitutability in inference as to 
existential matters by satisfaction of conjunct symmetrical- 
transitivity. In short, the import of instituting meanings which 
have this conjoint relativity is that it is the logical ground of the 
fundamental logical category of equivalence. This consideration 
alone makes it unnecessary to dwell upon the fact that no term 
has this relation as its inherent property, but that the relation ex- 
presses a condition to be satisfied in institution of meanings entitled 
to function in controlled inquiry. 

3. Correlation. For the purpose of inference and of ordered 
discourse, it is important in many problems that the relation be- 
tween relata-referents be determinate with respect to its scope, or 
its range and comprehensiveness. Correlation is the name techni- 
cally used to designate this form of order. In a monogamous legal 
system, the relation of husband-wife is one-one; in a polygamous 
system it is one-many; in a polyandrous system, it is many-one. 
A simple example of the force of the principle in inquiry is had 



FORMAL FUNCTIONS AND C AXONS 335 

when a man or woman is tried for bigamy. For it illustrates that 
the kind of "correlation" which holds among terms is conditioned 
upon the extent to which a given field of subject-matter has been 
systematically determined in prior inquiry, a result that is brought 
about only through abstract universal propositions as rules of 
operation. In the case cited, for example, only legal rules as to 
marriage determine the import of a given relation so that conse- 
quences may be inferred. 

The relation of friend-friend is symmetrical in a given or speci- 
fied case. But it is many-many. A and B are friends in a recipro- 
cal sense. But A may have C, D 7 E . . . as friends and B may 
have N, O, P . . . as friends. Nothing follows as to the relation 
of friendship, indifference, or enmity existing among these other 
terms as between friends of B and A. However, in the situation 
illustrated in the saying "Love me, love my dog," the relation of 
friend-friend is so conditioned that B cannot be a friend of A 
unless B is also the friend of C, who is a friend of A. This type 
of relation is exemplified in the case of some blood-kinship, blood- 
brotherhood, and secret-society relations, where each related mem- 
ber is bound to defend and support every other member, 
independently of prior acquaintance. The relation is still many- 
many, but a system is so constituted that the relation of transitivity 
holds between the elements of the system that have many-many 
relations taken severally. When the relation is not determined by 
co-presence in a system, the many-many relation is too indeter- 
minate to permit of transitivity. Mathematics is the outstanding 
exemplar of a system in which terms have many-many relations 
to one another, and yet the rules of operations determining the 
system are such that one-one relations can be instituted whenever 
it is necessary. 3 

4. Connectivity. Relational terms satisfy the condition of con- 
nexitivity whenever symmetrical terms are also transitive. Equiva- 
lence is, as we have seen, an instance of symmetrical transitivity, 
grounding, as it were, back-and-forth movement in inference and 
discourse. The term "connexitivity" may be extended to include 
such cases. Asymmetrical transitivity is exemplified in such terms 

3 Any cardinal number, for example, is both a sum (product, power) and 
also a unit factor and root with regards to other numbers. 



336 PROPOSITIONS AND TERMS 

as greater-than, hotter-than, and in comparative terms generally, 
in which terms have the relation of converse symmetry. Con- 
nectivity is not so much a coordinate relation as it is a complex 
of relations, the function of transitivity being basic in all modes 
of logical relation. 

The discussion has been conducted upon the basis of distinctive 
forms of the relative and relational terms that are commonly recog- 
nized. But these forms have been interpreted upon the doctrinal 
ground that the relations in question indicate either (1) formal 
conditions that terms (meanings) must satisfy in order to function 
in inquiry yielding warranted conclusions, or (2) as warnings that 
the conditions required have not been fulfilled. An example of 
the latter would be the case of asymmetrical intransitivity or the 
many-many relations in which elements have not been determined 
to be elements in an ordered system. It is difficult to avoid the 
impression in reading some logical texts (even those in which the 
necessity of strict formalism is emphasized) that meanings (terms) 
are taken just as they happen to present themselves in isolation 
and certain labels are then placed upon them. 

II. FORMAL RELATIONS OF PROPOSITIONS 

It has been noted that (1) terms are logically related in a propo- 
sition only as the proposition of which they are related members 
is itself in ordered relation to other propositions, and that (2) cer- 
tain terms have purely relational force, so that their meaning is 
wholly exhausted in their office of instituting relations between 
other terms. Terms that exemplify the latter condition are all 
the words that are grammatically called connectives, such as and, 
or, that (which), only (none but), etc. These strictly relational 
terms appear in propositions. But their logical force and function 
in a proposition, in its severalty, have to do with the function of 
that proposition in a set or series of related propositions — a logical 
character expressed in contemporary logic by calling the proposi- 
tions in which they appear "compound" propositions. 4 In other 
words, connectives represent satisfaction of the logical conditions 

4 According to the position developed in this book, the "simple" propositions, 
with which other propositions are contrasted as "compound," are logically in- 
complete, being instituted only for the sake of arriving at the complete proposi- 
tions which are called compound. 



FORMAL FUNCTIONS AND CANONS 337 

that are required to constitute any given proposition a member of 
an ordered set or series of propositions. 

It was shown in Chapter X that comparison-contrast is the 
means by which contents are determined in that relation which 
constitutes a proposition. It was also shown that comparison- 
contrast can be defined only in terms of the institution of con- 
jugately related affirmative and negative propositions, which 
express the results of operations of inclusion-exclusion. The scope 
and necessity of the latter operations in strict correspondence with 
each other, is such that propositions logically related to one another 
(in sets or series) must satisfy the formal conditions of conjugate 
exclusiveness-inclusiveness, or be conjunct-disjunct in relation to 
one another. The purely relational terms and, or, that, only, along 
with other formally relational terms, such as, if, then, either-one- 
or-other-but not-both, some, is, is~not, are the symbols by which 
are designated the conjunctive-disjunctive functions which render 
a given proposition formally capable of being a related member of 
a set or series of ordered proposition. However, not all of the 
relational terms listed stand on the same logical plane, or are of 
coordinate force. Some of them mark a relation that satisfies (or 
is taken as if it satisfied) the functions of conjunction-disjunction, 
while others mark contents still in process of complete determina- 
tion with respect to satisfaction of these functions — that is, mean- 
ings whose force is still problematic. "Any" is of the former type; 
"a or an" (when not a synonym of "any") and "some" are of the 
latter type, as are also "this? and "the" in the cases in which "the" 
is a synonym of this. 

The doctrinal conclusion reached may, accordingly, be formu- 
lated as follows: Sets and series of propositions are so ordered as 
to constitute in their functional correspondence (conjugate rela- 
tion) with each other a scientific system (one satisfying necessary 
formal conditions) only when taken severally they are co-alternate 
(exclusive) and, taken together, they are co-conjunct or inclusive 
and exhaustive. This formulation is intended, on one side, to state 
that the functions in question are not inherent properties of propo- 
sitions but are logical conditions to be satisfied; and, on the other 
side, that they are highly generalized logical "leading principles," 



338 PROPOSITIONS AND TERMS 

since they set forth operations to be performed which are logically 
basic. 

It remains only to introduce certain further distinctions, the 
most important of which are designated by words borrowed from 
mathematics but which are given logical meaning: namely, additive 
and multiplicative. Conjunction-disjunction is additive in appli- 
cation to existential subject-matter whether singular or generic; 
it is multiplicative in application to the interrelation of characters 
constituting abstract universal propositions. Illustrations will 
render the import of this statement evident. Additive summative 
conjunction is symbolized by and (of which a comma is often the 
logical equivalent) while additive alternate conjunction is ex- 
pressed by or. In the case of singulars, "and" as an additive con- 
junction constitutes a collection, as "This regiment is composed 
of this and that and the other enumerated person" until every 
member is listed. An instance of alternate additive conjunction of 
singulars is found in the following: "Any member of the Cabinet 
of the Federal Government is either Secretary of State, or of the 
Treasury, of the Interior, or . . ." until all members of the col- 
lection are listed. 

The logical force of and-or applied to kinds is different from 
this case of singulars. For example, such a proposition as that just 
stated (as to singulars composing a collection) is denied by deny- 
ing the presence of any one of the singulars listed, while its com- 
pleteness may be denied by affirming that some other singular 
should be added. In the case of kinds, denial applies to the 
relation of conjunction as such. The validity of the proposition 
"James, John, Robert and Henry were present on a given occa- 
sion" is impeached when it is shown that any one of the four was 
absent. The generic proposition "Birds, bats, butterflies are sub- 
kinds of one and the same inclusive kind" is invalidated whenever 
it is shown that the trait of being flying-creatures is not a con- 
junction of characteristics sufficient to determine an inclusive 
kind, and that differences in modes of flying are not sufficient to 
differentiate included kinds. Denial applies not to kinds taken 
severally but to the relation of inclusive-included; or, more strictly, 
to the set of generic differential characteristics by which kinds 
are determined as inclusive and included. 



FORMAL FUNCTIONS AND CANONS 339 

The proposition "Birds, fishes, reptiles, simians, human beings, 
... are vertebrates," is a summative conjunctive proposition 
about relations of kinds in forming an including kind. The al- 
ternate conjunctive form of proposition is "Vertebrates are birds 
or fishes or reptiles or simians or human beings or . . ." It might 
seem as if the difference were merely linguistic, not logical, con- 
sisting simply in the fact that in the case of summative addition 
(expressed by and) sub-species are enumerated first, and in the 
case of logical addition by alternates (expressed by or) the in- 
cluding kind is stated first. There is, however, a genuine logical 
difference. There is nothing in the case of summative addition 
taken apart from the alternative form to warrant either the com- 
pleteness (sufficiency) of the included kinds in relation to the 
inclusive kind, or their non-overlapping character. The logical, 
as distinct from the verbal, force of or consists in satisfaction of 
the condition that the kinds which are summatively added do not 
overlap, being described by differential characteristics. Take for 
example, the proposition: "Birds and whales and mammals are 
vertebrates." Since whales and mammals are defined by the same 
set of traits, "and" does not here determine exclusion. The logical 
force of or means the necessity for institution of sub-kinds that 
are descriptively determined by traits that are so differential as to 
be reciprocally exclusive within the set of characteristics describing 
the including kind. Kinds connected by and may constitute 
propositions valid as far as they go but that are not sufficiently 
inclusive. 

So far it has been assumed rather than shown that the additive 
function in its summative and alternative modes applies only to 
the relation of terms in propositions having existential reference. 
The simplest way of showing the validity of the position taken is 
to consider the relation of characters which constitute the content 
of a universal non-existential proposition. In the case of charac- 
teristics describing kinds, whether including or included, it is 
necessary that the traits employed be materially independent of 
one another and yet so involved that in cumulative conjunction they 
form a set of traits that suffice to determine kinds inclusively 
and exclusively. The relation of characters in an abstract propo- 
sition is, on the other hand, an interrelation. Only as the meaning 



340 PROPOSITIONS AND TERMS 



of each character is constituted in reciprocal dependence upon all 
other characters involved does a universal proposition satisfy 
logical conditions. It is this form of relationship which is desig- 
nated by the term multiplicative. The conjunction in question is 
not of contents that are capable of independent observation or 
independent determination. The "conjunction" is one of "na- 
tures" not of traits. The necessity of the relation marking univer- 
sal propositions in distinction from the contingency of existential 
propositions is constituted by the multiplicative conjunction of its 
related characters. 

Being mammalian, for example, is determined by the multipli- 
cative conjunction of the characters, warm-blooded, viviparous 
and suckling young. If this universal proposition is valid as a defi- 
nition, it is (1) independent of the existence of creatures marked 
by corresponding qualitative traits; while (2) it involves the idea 
that these characters are necessarily interrelated, so that any one 
of the three characters is meaningless in the definition apart from 
its modifying and being modified by the other terms. In other 
words, if warm-blooded, then viviparous, etc. Suppose, however, 
a proposition about a relation of kinds were as follows: "Mam- 
mals are warm-blooded, and (or) viviparous, and (or) offspring- 
suckling." It is clear, on its face, that such a proposition is a dis- 
guised definition of being mammalian. 

Alternate multiplication is necessary to determine sufficiency 
in the case of the relation of characters, as in the case of the con- 
junction of characters describing related kinds. Irrelevant and 
superfluous characters must be ruled out. In the case, say, of the 
conception of triangularity magnitude is excluded from the defi- 
nition, while shape is no part of the conception outside the limits 
determined by the relations of the characters of right-angularity, 
equilateralness and scaleness. This conception is now so stand- 
ardized that elirnination of these characters may seem too trivial to 
be worth mentioning. But there was a time when inquiry into 
geometrical relationships was retarded because size was thought 
to be a necessary property of triangles. For as long as triangles 
were supposed to have existential reference, size ivas a generic 
trait. If we take the relations of characters that define, say, being 
metallic, completeness of the characters in question can be de- 



FORMAL FUNCTIONS AND CANONS 341 

termined only as they are disjoined from characters whose inter- 
relation defines being chemically elemental in other ways than 
being metallic as well as in ways that are reciprocally exclusive. 
To repeat in this context a point made in other contexts: When 
it is affirmed that triangularity is either right-angular, scalene or 
isosceles, it is affirmed (1) that these ways of being triangular 
exhaust all the possibilities of relationship of the lines and angles 
in question, and (2) that the relationships constituting being 
triangular are so interrelated that these ways of being triangular 
are necessary to the conception of the triangular. 

Functional correspondence of propositions which satisfy re- 
spectively the conditions of additive and multiplicative conjunc- 
tion-disjunction is necessary for final warranted judgment. Only 
copulation of propositions of subject-contents and predicate con- 
tents determines, on one side, that the universal propositions em- 
ployed are operationally relevant, and, on the other side, that the 
conjoined traits used to describe kinds are exclusive-inclusive be- 
cause of a ground or reason. For otherwise the basis of their 
conjunction is merely recurrent observations, so that the con- 
junction observed constitutes a problem. The logical form of 
the conjugate correspondence is expressed in the relational terms 
"either-one-or-other-but-not both." Take the following proposi- 
tion: "Mankind consists of Europeans, Africans, Australians, 
Americans . . ." where . . . indicates that addition is summa- 
tively exhaustive. There is nothing in the proposition as it stands 
to preclude hyphenated membership, or kinds that are, say, 
European-American. Only a rule expressed in a universal propo- 
sition can determine such kinds that this possibility is ruled out. 
Such a determination is not particularly important in the example 
selected, although the question of dual political citizenship may be 
an actual one. But there are scientific inquiries in which it is 
indispensable to determine that kinds are related so that any 
singular must be of one-or-another kind but-not-of-more-than- 
one. Indeed, satisfaction of this condition is necessary to any 
valid set of disjunctive propositions. It cannot be achieved except 
upon the basis of a set of disjunctive universal-hypothetical propo- 
sitions whose operational application determines kinds exclusive of 
one another within an exhaustive including kind. 



342 PROPOSITIONS AND TERMS 

1. Certain corollaries follow. It is usual in texts to find such 
propositions as have been considered termed "compound," where 
"compound" postulates "simple" propositions that are prior to and 
independent of the conjunctive-disjunctive function. But from 
the position taken (namely, that any symbolic expression has the 
logical status of being a proposition only as a member of an or- 
dered set or series) it follows truistically that there are no "simple" 
propositions in the sense alleged. There are, of course, proposi- 
tions that are relatively simple. But they have logical status only 
in institution of so-called "compound" propositions. For exam- 
ple, a particular proposition, one about a change which at a given 
time is incapable of analysis into a complex of interactions, is a 
simple or elementary proposition. But (1) it is only conditionally 
such, for its determination depends upon the available techniques 
of experimental observations. As these improve, changes which 
are more elementary may be discovered, while (2) in any case 
their simple nature is functional. For its content as simple is deter- 
mined by its capacity to serve as a condition in delimitation of a 
problem. Hence the degree of "simplicity" required varies with 
the problem in hand. 

2. Save as the conjugate nature of the functions of additive- 
multiplicative conjunction-disjunction is acknowledged there is no 
logical ground for making a distinction between division and 
classification. The process is then called "division" when it pro- 
ceeds from the inclusive kind to the included kinds, and 
"classification" when the movement is in the reverse direction. 
Subject-matter is identical in both cases. If, however, "division" 
in its logical sense is reserved for discrimination of differential 
traits describing mutually exclusive kinds within the more com- 
prehensive conjunction of traits that describe an including kind, 
it has a distinctive logical meaning. "Classification" would then 
be used to stand for the discriminated interrelation of characters 
that mark off "classes" (in the unambiguous sense of categories) 
within the comprehension of the category of the widest applica- 
bility. "Division" is applicable to kinds in extension and "classi- 
fication" to conceptions in comprehension. 

3. The classic theory of genus and fixed included species fur- 
nished an ontological ground for definition. The latter consisted 



FORMAL FUNCTIONS AND CANONS 343 

of statement of the genus and the differentia which together 
marked off and identified the species in question. Abandonment 
of the cosmological ground for this conception of definition left 
the logical status of definition in the air. It has been treated, for 
example, as a purely linguistic matter in which the meaning of a 
single word is set forth in a set of words whose several meanings 
are taken to be already understood. Taken literally, this concep- 
tion leaves the combination of the defining words wholly unex- 
plained and ungrounded. And yet it is in virtue of their 
conjunction, additive or multiplicative, that they form a definition, 
either in the sense of description of a kind or in the stricter sense 
of analysis of an abstract conception. That symbols, of which 
words in their ordinary sense are a limited kind, are necessary to 
definition, and that in a definition a single symbol having a total 
meaning is resolved into an interrelation of meanings is sound doc- 
trine. It provides the element of plausibility in the merely lin- 
guistic interpretation of definition. 

But the logical import of definition is radically different. Con- 
ceptual meanings are instituted in their office as representatives of 
possibilities of solution. They are capable of performing this of- 
fice only as they are resolved into characters that are necessarily 
interrelated just because they are an analysis of a single conception. 
The value (validity) of any given analysis of any given conception 
(this analysis being the definition) is finally fixed by the power of 
the interrelated characters to institute a series of rigorous sub- 
stitutions in discourse. Only such a conception of definition ac- 
counts for the indispensable role played by definitions in inquiry, 
and explains how and why a given selection and conjunction of the 
terms of a definition is logically grounded instead of being arbitrary 

III. FORMAL CANONS OF RELATIONS OF PROPOSITIONS 

The functions of additive and multiplicative conjunction-dis- 
junction go back, as we have seen, to the conjugate relation of 
affirmation-negation, inclusion-exclusion. Hence they may be fur- 
ther generalized. When so generalized, the fundamental functions 
involved take the form of logical principles to which the name 
Canons is traditionally applied. These canons are Identity, Con- 
tradiction and Excluded Middle. On the ground of the position 



344 PROPOSITIONS AND TERMS 

taken, it follows truistically that they express certain ultimate 
conditions to be satisfied, instead of being properties of proposi- 
tions as such. Upon the basis of the cosmological-ontological 
assumptions of the classic logic, it was a sound logical doctrine 
that treated identity, etc., as necessary structural properties. Spe- 
cies, which alone were capable of definition, classification, and 
scientific demonstration, were immutable. Hence they were in- 
herently self-identical. Any species is always and necessarily just 
what it is. The canon of identity expressed symbolically in the 
form A is A was, accordingly, the proper form in which any 
proposition having scientific status should be stated. Species were 
also ontologically exclusive of one another. No transitions or 
derivations were possible among them because of their necessary 
ontological exclusion of one another. Hence, tertiwm non datur. 5 
1. Identity. From the standpoint of the position that it is nec- 
essary for propositions to satisfy conditions set by membership in 
a set or a series of propositions, identity means the logical require- 
ment that meanings be stable in the inquiry-continuum. The 
direct and obvious meaning of this statement is that a meaning 
remain constant throughout a given inquiry, since any change in 
its content changes the force of the proposition of which it is a 
constituent, thus rendering it uncertain upon what meanings and 
relation of meanings the conclusion reached actually depends. 
Fulfilment of this condition does not mean, however, that a given 
symbol shall have the same meaning in all inquiries. If it did have 
this meaning, progress in knowledge would be impossible. But 
the judgment which is the final issue of inquiry modifies to some 
extent, sometimes crucially, the evidential import of some observed 
fact and the meaning previously possessed by some conception. 

5 That Aristotle's formulation of the principle of contradiction is somewhat 
equivocal is frequently noticed by modern exponents of his logical doctrine. 
It would seem to be a combination of two considerations; one, that any con- 
tradiction violates the principle of the necessary identity of a species; the other, 
that contrary propositions not only exist in the case of changes, as signs of lack 
of complete Being, but are inevitable, since in his cosmology it is the hot which 
becomes cold, the moist which alters into the dry, etc. Plato, without formulat- 
ing the principle of contradiction, had argued against the complete reality of 
change on the ground that if it had a full measure of Being contradictory 
propositions were inevitable, since it then followed that something both was 
and was not. On the whole, contradiction seems to have been employed as 
evidence for the principle of identity rather than as an independent principle. 



FORMAL FUNCTIONS AND CANONS 345 

Unless identity has functional force in relation to the subject- 
matter undergoing inquiry, the canon of identity is violated in 
every scientific advance. 

The deeper and underlying import of the principle of identity 
is, accordingly, constituted in the very continuum of judgment. 
In scientific inquiry, every conclusion reached, whether of fact 
or conception, is held subject to determination by its fate in further 
inquiries. Stability or "identity," of meanings is a limiting ideal, 
as a condition to be progressively satisfied. The conditional status 
of scientific conclusions (conditional in the sense of subjection to 
revision in further inquiry) is sometimes used by critics to dis- 
parage scientific "truths" in comparison with those which are 
alleged to be eternal and immutable. In fact, it is a necessary 
condition of continuous advance in apprehension and in under- 
standing. 6 

2. Contradiction. The logical condition to be satisfied for the 
canon of contradiction is independent of that of identity, although 
necessarily conjunctive with it. Violation of the principle of 
identity may lead to contradiction. But the logically important 
instances are those in which observance of the principle of identity 
results in a contradiction. For establishment of propositions 
one of which must be valid if the other is invalid is an indispen- 
sable step in arriving at a grounded conclusion. 7 Contradiction 
is not then just an unfortunate accident which sometimes happens 
to come about. Complete exclusion, resulting in grounded dis- 
junction, is not effected until propositions are determined as pairs 
such that if one is valid the other is invalid, and if one is invalid 
the other is valid. The principle of contradiction thus represents 
a condition to be satisfied. Direct inspection of two propositions 
does not determine whether or not they are related as contradic- 

6 The best definition of truth from the logical standpoint which is known to 
me is that of Peirce: "The opinion which is fated to be ultimately agreed to by 
all who investigate is what we mean by the truth, and the object represented by 
this opinion is the real." Op. cit., Vol. V, p. 268. A more complete (and more 
suggestive) statement is the following: "Truth is that concordance of an ab- 
stract statement with the ideal limit towards which endless investigation would 
tend to bring scientific belief, which concordance the abstract statement may 
possess by virtue of the confession of its inaccuracy and one-sidedness, and this 
confession is an essential ingredient of truth." (Ibid., pp. 394-5). 

7 Cf. ante, pp. 195-8 and pp. 337-41. 



346 PROPOSITIONS AND TERMS 



tones, as would be the case if contradiction were an inherent rela- 
tional property. The contrary doctrine is often affirmed, as when 
it is said that the two propositions A is M and A is not M directly 
contradict each other. But unless A has already been determined 
conjunctively-disjunctively, by prior inquiry, some part of A, or 
A in some relation, may be M, and some other part of A, or A 
in some other relation, may be not M. The relation of A to M 
and not M can be determined only by operations of exclusion 
which reach their logical limit in the relation of contradiction. 

3. Excluded Middle. It was stated earlier that complete satis- 
faction of the conditions of conjunctive-disjunctive functions, 
additive and multiplicative, is formally represented in the form 
either-one-or-other-but-not-both. The principle of excluded mid- 
dle presents the completely generalized formulation of conjunctive- 
disjunctive functions in their conjugate relation. The notion that 
propositions are or can be, in and of themselves, such that the 
principle of excluded middle directly applies is probably the source 
of more fallacious reasoning in philosophical discourse and in 
moral and social inquiries than any other one sort of fallacy. 
That fact that disjunctions which were at one time taken to be 
both exhaustive and necessary have later been found to be in- 
complete (and sometimes even totally irrelevant) should long ago 
have been a warning that the principle of excluded middle sets 
forth a logical condition to be satisfied in the course of continuity 
of inquiry. It formulates the ultimate goal of inquiry in complete 
satisfaction of logical conditions. To determine subject-matters 
so that no alternative is possible is the most difficult task of in- 
quiry. 

It is frequently argued today that the three principles in ques- 
tion have become completely outmoded with the abandonment of 
their foundations in the Aristotelian logic. The Aristotelian in- 
terpretation of them as ontological, and any interpretation which 
regards them as inherent relational properties of given proposi- 
tions, must certainly be abandoned. But as formulations of formal 
conditions (conjunctive-disjunctive) to be satisfied, they are valid 
as directive principles, as regulative limiting ideals of inquiry. An 
example sometimes put forward to show the meaninglessness of 
the principle of excluded middle is its inapplicability to existences 



FORMAL FUNCTIONS AND CANONS 347 

in process of transition. Since all existences are in process of 
change it is concluded that the principle is totally inapplicable. 
For example, of water that is freezing and of ice that is melting, 
it cannot be said that water is either solid or liquid. To avoid this 
difficulty by saying that it is either solid, liquid or in a transitional 
state, is to beg the question at issue: namely, determination of the 
transitional intermediate state. The objection is wholly sound on 
any other ground than that the canon expresses a condition to be 
satisfied. But taken in the latter sense, it shows the scientific 
inadequacy of the common sense conceptions of solid and liquid. 
As scientific existential inquiry has become occupied with changes 
and correlations of change, the popular qualitative ideas of solid, 
liquid, gaseous states have been expelled. They are now replaced 
by correlations of units of mass, velocity and distance-direction 
formulated in terms of numerical measurements. The necessity 
of instituting exclusive disjunctions, satisfying the condition of 
excluded intermediates, has been a factor in bringing about this 
scientific change. 

This chapter has been concerned with formal conditions which 
propositions must satisfy in order to fulfil their functions in in- 
quiry. The logical conditions in question concern, on one side, 
sets of propositions in the relations which ground an inferential 
conclusion, and, on the other side, series of propositions in the 
relations that constitute ordered discourse. In each case, the con- 
cluding proposition is said to "follow" from preceding propositions 
while the reverse process is called "going or proceeding from." 
The nature of the "following" is different in inference and in 
discourse. The traditional (and essentially conventional) state- 
ment of the difference is that in the former we go from particular 
propositions to the general, and in the other from the general to 
the particular. This mode of statement had genuine import and 
foundation in the Aristotelian logic. But it lacks both ground 
and logical meaning in scientific inquiry as that is now carried on. 
A conclusion in mathematical discourse is as universal (since it is 
an abstract hypothetical proposition) as are those from which it 
follows. While it may have less comprehension, or scope of ap- 
plicability, it may also have greater or less comprehension, ac- 



348 PROPOSITIONS AND TERMS 

cording to the exigencies of the problem in hand. The idea that 
general propositions are arrived at by "going" from particular 
ones is more plausible, since particular propositions are necessary 
in order to formulate the problems that required general proposi- 
tions for their solutions. But formulation of the operations that 
determine a generalization with respect to particulars is much 
more complex than can be covered by the words "following" or 
"going." The institution of the general proposition includes, for 
example, performance of operations prescribed by the idea of a 
possible solution such that facts not previously observed are their 
consequences. The nature of the "going" and the "following" 
which are involved constitutes a logical problem which carries 
logical discussion into the subject of the nature of scientific method. 
It involves specifically the problem of the nature of induction and 
deduction and their relations to each other. The field thus indi- 
cated forms the subject of Part III and will be taken up after the 
discussion of Terms found in the next chapter. 



CHAPTER XVI11 
TERMS OR MEANINGS 



In older logical texts it was the usual practice to deal first with 
terms, then .with propositions and finally with propositions 
ordered in relation to one another. According to the position 
developed in this book, the procedure is reversed, for inquiry, in- 
volving propositions so determined and arranged as to yield final 
judgment, is the logical whole upon which propositions depend, 
while terms as such are logically conditioned by propositions. It 
follows that the discussion of terms undertaken in this chapter in- 
troduces no new principles. Special discussion of terms may, 
however, serve to review and clarify some of the conclusions al- 
ready arrived at. The word "term" was used by Aristotle to 
designate an elementary constituent of a proposition as its bound- 
ary; and the word term is derived from the Latin terminus mean- 
ing both boundary and terminal limit. Like other boundaries, for 
example those of political institutions and tracts of real estate, 
terms both demarcate and connect, and hence no term has logical 
force save in distinction from and relation to other terms. 

This statement is not contradicted by the fact that all familiar 
words carry some meaning even when uttered in isolation. They 
have such meaning because they are used in a context in which 
relation to other words is involved; furthermore, their meaning 
is potential rather than actual until they are linked to other words. 
If the words sun, parabola, Julius Caesar, etc., are uttered, a line 
of direction is given to observation or discourse. But the objective 
of the direction is indeterminate until it is distinguished from 
alternative possible terminations, and is thus identified by means 
of relation to another term. Uncertainty as to boundaries is the 
source of disputes and conflicts about meanings. Indeterminate 
terms either claim too much and are loose because overlapping, 

349 



350 PROPOSITIONS AND TERMS 

or are too restricted and result in an unoccupied no-man's-land. 
In other words, no term can be fully determinate save as the 
terms to which it is related are also determinate in both conjunctive 
and disjunctive reference. Terms, as logical limits, look, like other 
boundaries, in two directions. They are settled as the outcome of 
prior activities and they exercise jurisdiction in further inquiries. 
They possess both of these traits and exercise both of these func- 
tions in their capacity of instruments. Like all instrumentalities 
they are modifiable in further use. 

Traditional texts on logic have usually distinguished between 
terms as concrete and abstract; denotative and -connotative; ex- 
tensive and intensive; singular (plural), collective and general. 
These recognized distinctions will be taken as the material of 
discussion. But their interpretation on the ground of the prin- 
ciples formulated in previous chapters will necessarily differ in 
important respects from that which is traditional. It will also 
involve introduction of some additional distinctions, as for exam- 
ple, resolution of general terms into generic and universal. In its 
departure from traditional interpretations, the discussion also in- 
volves disagreement with some recent texts that have also departed 
from tradition. For example, some texts make a sharp distinction 
between names and terms on the ground that names are designa- 
tions of subject-matters which are irrelevant to strict logic while 
terms are purely formal. Strictly adhered to, this position would 
eliminate completely all so-called "concrete" terms and would also 
exclude all existential propositions since the latter ultimately in- 
volve either proper names or some equivalent expression such as the 
demonstrative "this." 

The texts in question are never wholly consistent in this matter. 
In further distinction from them the position here taken involves 
the impossibility of making a sharp division between form and 
subject-matter. For it holds that subject-matter is what it is in 
virtue of its determination by the forms which make inquiry to be 
what it is, while forms in turn are adapted to institution of subject- 
matters such as serve the requirements of controlled inquiry. 
There are other schools that limit the application of names to 
existential things and which therefore assign to terms a wider scope. 
But names are designations by means of symbols. And while it is 



TERMS OR MEANINGS 351 



fundamentally important to note whether what is designated by a 
symbol is material or is formal (as in the case of and-or), it is 
purely arbitrary to hold that the latter words do not designate or 
name what they do designate, namely formal relations. It seems 
to be a superstition taken over from traditional grammar that a 
name must designate something concrete. In fact every symbol 
names something; otherwise it is totally without meaning and is 
not a symbol. A diagram or a map has some reference and desig- 
native force, even though linguistic usage does not treat either of 
them as a name. 

The basic distinction of terms which is here proposed follows 
from the theory of judgment. Any given term applies ultimately to 
the content of either subject or predicate of judgment; it is either 
existential or conceptual in reference. All other distinctions are 
either aspects of this fundamental distinction in logical office or are 
derived from it. A simple example of this distinction occurs be- 
tween the following terms. 

1. Concrete and Abstract Terms. Words designating imme- 
diately experienced qualities are concrete par excellence. For ex- 
ample, sweet, hard, red, loud when they are used to characterize 
observed subject-matter so as to discriminate and identify it: that 
is, as evidential marks or signs. Demonstrative words, this, that, 
now, then, here, there, are also concrete. So are common nouns 
which designate kinds, and such adjectives as designate character- 
istics by which kinds are identified and discriminated. Abstract 
words are such as stand for conceptions, including relations which 
are taken without reference to actual application to things, for 
example, sweetness, solidity, redness, loudness, presence, absence, 
position, location, fatherhood, angularity, etc. While certain 
endings, such as ity, ness, tion, differentiate abstract nouns from 
common nouns, there are many words which are abstract or con- 
crete according to the context in which they function, independ- 
ently of verbal endings. Color and sound, for example, are con- 
crete when they refer to traits that are properties of existential 
objects, but in science they are abstract, meaning colority or 
visibility and audibility as possibilities. In order to be applicable 
in directing scientific inquiry they are defined in terms of nu- 
merical rates. Many adjectives are striking instances of indeter- 



352 PROPOSITIONS AND TERMS 



minateness with respect to the difference in question. As applied 
directly to things they are of course existential, but they may also 
stand for simple possibilities. The words circular or oblong are 
concrete when used to describe actual objects, as in "circular 
saw" or "oblong table." In mathematics, circle means circularity, 
and oblong means rectilangularity. As the example shows, nouns 
that are formed from adjectives may be abstract in use without 
indicating that form when the word does not function in a given 
proposition. Thus "solid" may be used to characterize things 
in distinction from "liquid," while in mathematics it designates a 
character which defines possible ways of being figurate in distinc- 
tion from the way designated by plane. 

Traditional nominalistic empiricism has tended to treat abstrac- 
tion as such as "vicious" when taken to be other than a convenient 
linguistic procedure for referring to a number of singulars having 
a "common quality." Even now, it is regarded as a mark of 
sophistication to contemn an abstract word because a concrete 
"referent" cannot be pointed out. There is without doubt great 
abuse of abstractions, but it is to be corrected by noting that their 
referents are possible modes of operating. The counterpart logical 
error is that an abstraction is mere selection of a universal quality 
already possessed by objects. Then it is said that the abstract idea 
of smoothness arises from apprehending the quality "smooth" 
apart from any particular thing that possesses it. The universal, 
smoothness, according to this view is logically prior to the concrete 
smooth, the latter being an embodiment of the universal in a sin- 
gular. Generalized, this view holds that all qualities and all rela- 
tions are intrinsically universal, even such qualities as sweet, hard, 
red, etc., as well as such relations as are expressed by active verbs 
which connect existential objects together, as kill, eat, give. In 
"Brutus murdered Caesar" for example "murdered" is regarded as 
having the same logical form as is has when it is affirmed that 
"Honesty is a virtue"; or that the form of "different from" is 
identical when it is affirmed that "Pride is different from conceit," 
as it is when it is said "This object is different from that in shape, 
or size," etc. 

We cannot arrive at the abstract from the concrete merely by 
considering a quality apart from other qualities with which it is 



TERMS OR MEANINGS 353 

conjoined in a thing. There exists, we shall say, a horse which 
is roan, male, five years old and fifteen hands high. We can select 
any one of these qualities for further consideration without think- 
ing of, or inquiring into, other qualities. For example, if a buyer 
is considering buying a horse to form one of a team, his inquiry 
may attach itself either to color or height or age as matters which 
decide whether or not the two horses w T ill "go well" together. 
But the quality still remains "concrete." Roan is not roanness; 
so-many-years-old is not age as an abstraction; so-high is not tall- 
ness. The comparison in which a given quality is selected out of 
a complex is a condition of abstraction, but the quality selected is 
not, on that account, a universal. Moreover, a quality is not a uni- 
versal merely because it characterizes a number of singulars. In that 
capacity it serves, like any trait, to describe a kind. To become a 
universal it must be so defined as to indicate a possible mode of 
operation. Its function is to determine the characteristics which 
must be found to exist in order to warrant the inference that a 
given singular is of specified kind. Genuine illustrations of ab- 
straction are found in the conception of heat as a mode of molecu- 
lar motion; just as a pseudo-abstraction is found in the old con- 
ception that heat is califoricity — which only repeats in an abstract 
word the experienced quality. The quality smooth is warrantably 
affirmed of objects only as the universal, smoothness, is such as to 
prescribe operations of technical measurement. The common 
sense conception of smoothness, derived from operations executed 
by touch and sight, serves many ordinary practical ends but is in 
no sense a scientific conception. Only a mathematical formula 
defines smoothness. It can no more be derived from directly 
experienced qualities by selection, inspection and comparison of 
them than the definition of heat as molecular motion can be de- 
rived from direct inspection and comparison of the quality of 
various hot things. 

2. Singular, Generic and Universal Terms. Each conceptual 
term of predicative force is universal since it designates an opera- 
tion possible of performance, independently of whether the condi- 
tions to which it applies are actually observed or not. Singular 
and generic terms are existential in reference and are conjugate. 
The individual as such is a unique nonrepeatable qualitative 



354 PROPOSITIONS AND TERMS 

situation. The singular, represented, say, by this, is a subject- 
matter discriminate^ selected from a total qualitative situation so 
as to serve the function of determining a problem and providing 
facts which, as evidence, test any proposed solution. As has been 
previously said, qualities are not recurrent in themselves but in 
their evidential function. As evidential, they are characteristics 
which describe a kind. Consequently, singular and generic repre- 
sent two emphases of a subject-matter of a proposition which has 
existential import. "This is a meteorite" is singular with respect 
to this; generic with respect to meteorite. Context determines 
upon which of the conjugate forms emphasis falls in a given case. 
When meteorites are included within a more extensive kind, the 
proposition is that of a relation of kinds. There is no explicit 
reference to a singular or this; the proposition holds, if valid, in- 
dependently of whether any meteorite is observed to exist at this 
or that particular time and place. But the proposition postulates 
that meteorites do exist at some time and place. Thus it possesses 
a conjugate, although indirect, reference to singulars. The case 
is not otherwise when it is said that "Ogres are fabulous animals." 
It postulates the existence of fabulous or mythical beliefs, and 
affirms that belief in ogres has existed and that such beliefs are of 
the kind called fabulous, since observation has not established the 
existence of ogres although it warrants affirmation of the existence 
of beliefs about them. 

"General" as a logical term is ambivalent. As has been re- 
peatedly noted, it is employed to designate both the generic and 
the universal. The confusion of the two and its consequences in 
logical doctrine, namely, failure to observe the logical difference 
of the existential and non-existential, the factual and ideational, 
have been dealt with. We append, however, some comments 
upon the double meaning of the word law. It is employed to 
designate the content of physical generalizations both when (1) a 
specified conjunction of traits has been observed and confirmed 
without an exception being found, and (2) when the relation in 
question is itself a member of a system of interrelated universal 
propositions. In the former case, it designates what we call a 
general fact, such as "tin melts at the temperature of 232° C." 
There is no objection to the double use of the word "law." But the 



TERMS OR MEANINGS 355 

use should not be allowed to disguise the fact that law in one case 
is existential in reference, while in the other it is definitely non- 
existential in reference. A law in mathematical physics is uni- 
versal in as far as its mathematical content enables deduction to 
other propositions in discourse to be made. As a law of physics, 
its content is existential and contingent. 

3. Denotative and Connotative Terms. The logical difference 
between these two kinds of terms is once more that between terms 
of subject-content, which has existential reference, and terms of 
predicative and conceptual import. Terms are denotative when 
they refer, directly or indirectly (as in propositions of a relation of 
kinds) to existence. Common nouns, demonstratives, and verbs that 
denote change or action are denotative. Mill revived the scholastic 
term "connotation" (giving it, however, a different and confused 
meaning) to designate the adjectival contents which constitute 
the meaning of a generic term, stating that connotation determines 
the meaning of such terms. According to this view one and the 
same term is both denotative and connotative, with some definite 
exceptions to be noted hereafter. Thus, "ship" is denotative in 
respect to its application to an indefinite number of objects, while 
its connotation consists of the traits which any object must possess 
in order that the term ship can be warrantably applied to it. The 
confusion here involved is not particularly subtle. It is between 
characteristics which are the meaning of ship as a denotative term 
and the characters which ground, inclusively and exclusively, the 
logical capacity of traits to describe a kind. The first is de facto. 
It states the set of traits which are in empirical fact used as the 
ground of calling an object a ship instead of, say, a canoe or yacht. 
When questions arise as to whether or not a certain object is of the 
kind "ship," a definition of what it is to be a ship is demanded. 
Suppose the definition consists of the following (multiplicative) 
conjunction of characters; floating on water, having curved sides, 
of sufficient capacity to transport a considerable number of goods 
and persons, and being used regularly for commercial transporta- 
tion of goods and passengers. Such a term is not descriptive of 
traits which form the meaning of ship; they are prescriptions of the 
traits an object should have if it is to be a ship. The terms in 



356 PROPOSITIONS AND TERMS 

question are all abstract. They define shipness; they do not de- 
scribe existential ships. 

When connotation is restricted to the meaning of a denotative 
term (as it must be when a term is said to be both denotative and 
connotative) exactly the same thing is said twice. Ship as a term 
denotes primarily a set of traits and secondarily denotes a kind of 
objects because they are marked by these traits. When it is said 
that connotation determines the applicability of a set of traits to 
describe the kind, inquiry has moved into another logical dimen- 
sion, that of abstract universals. If "connotative" means some- 
thing other than descriptive, then the same term cannot have both 
denotation and connotation. Existential terms are denotative; 
abstract terms are connotative. Every denotative term is related 
to a corresponding or conjugate connotative term as far as its 
denotative capacity is warranted — substantially the scholastic use 
of connotation. If instead of ship, whose meaning is more or less 
conventional, we had taken a scientific term, such as chemical 
element^ or metal, the dependence of grounded denotative applica- 
tion upon defining conceptions of being chemically simple and be- 
ing metallic would be obvious. When a descriptive term is said to 
possess connotation in addition to denotation, not only is there 
bald repetition but no place is left for attributive terms or abstract 
universals. The word "connotation" should either be dropped 
or be reserved for the latter. 

The following quotation from Mill, whose loose use of the word 
"attributes" to designate both characteristics and characters is 
unfortunately followed by writers who do not agree with his basic 
postulates, illustrates the confusion discussed. When it is cleared 
of confusion, the quotation exemplifies both the difference and the 
relation of descriptive terms and prescriptive "connotative" terms. 
"The word man denotes Peter, Jane, John and an indefinite 
number of other individuals, of whom, taken as a class (kind) it is 
the name. But it is applied to them because they possess, and to 
signify that they possess, certain attributes. These seem to be 
corporeity, animal life, rationality, and a certain external form, 
which for distinction we call the human." x 

According to his official doctrine, the "connotation" ought to be 

1 Mill, Logic, Book I, Ch. 2, Sec. 5. 



TERMS OR MEANINGS 357 



simply the set of existential qualities which constitute the meaning 
of the general term "men." In that case, however, the concrete 
word "men" simply possesses a dual denotation; namely, one point- 
ing both to certain qualities used as marks and also to the objects hav- 
ing these qualities. It is accordingly significant that Mill actually 
illustrates connotation by means of abstract words, corporeity, 
rationality, which are not possessed properties of the objects in 
question, but which do have the force of indicating what qualities 
(namely, possession of a body and of power to reason) must be 
traits of objects if the name men is properly applied to them. For 
existent objects no more are or have corporeity and rationality 
than a sunset is or has redness. 

Mill's denial that proper names are connotative is thus correct 
on the basis of the interpretation of connotation just given 
(namely, that it belongs to abstract terms) and incorrect on the 
ground of his own theory. For proper names are certainly not 
abstract; there is nothing about them which determines the ground 
and right of their applicability to singulars. But since Mill has 
identified connotation with the meaning of a word, his denial 
signifies that proper names have no meaning whatever. At the 
same time, he assigns meaning to generic terms, which, according 
to him, are only collections of singulars. However, aside from this 
inconsistency, denial of meaning to a proper name deprives it of 
that denotative force with respect to a singular which Mill never- 
theless holds it does possess. If such words as London, Rocky 
Mountains, (which certainly are not names of abstract attributes) 
had no meaning, they would not be symbols or names at all. They 
would be mere noises having no application to one thing more 
than to any other. To all appearances, Mill's position rests upon a 
confused mixture of two different things. There are causes why 
the proper name "London" is applied to a given singular thing; 
there are no reasons, in the sense of logical ground, for its applica- 
tion. As to rationale the word lacks meaning. Moreover, while 
there are causes why the object to which the proper name is ap- 
plied is what it is, there is no logical ground for its having just the 
qualities it does in fact have. On the other hand, while there is no 
logical ground (but only historical causes) for the general term 
"horse" as a word being used to designate a kind of objects, there is 



358 PROPOSITIONS AND TERMS 

logical ground or reason for the selection of the special set of 
traits employed to describe horses qua a kind. In the sense of 
rationale or ground, the term or name "horse" has a kind of mean- 
ing which "London" does not have. But London or any proper 
noun does have a referent and it consequently has meaning in the 
sense of designating the distinctive traits which mark off and 
identify the singular to which it refers. 

Mill's essential error has been revived in another form by writers 
on logic, who are critics of Mill's views in general, in their denial 
that "this" has descriptive qualification. I shall not repeat the 
criticisms already made of the view which holds to a sharp logical 
distinction between the demonstrative and the descriptive. But 
two arguments that are advanced in support of the separation may 
be referred to. One of them is the confusion (previously pointed 
out) between an indeterminate descriptive qualification and a 
determinate one, as in the case of dispute whether "it" — an object 
seen at sea — is a mountain or a cloud. That such cases occur can- 
not be doubted. But their occurrence does not prove that "&" 
is wholly lacking in meaning. It only shows that its qualities, 
so far as yet observed, do not suffice for a grounded proposition as 
to its kind. The case does not differ, save in degree, from a case 
in which the object is warrantably affirmed to be a mountain, while 
a question still exists as to what kind of a mountain it is. It should 
be evident that unless there are some observed qualities constituting, 
in the instance cited, means for identification of "this" — there is 
no ground for holding that the two persons who differ as to the 
kind of which this is, are referring to one and the same "this." 
Unless they are, it is obvious that both propositions may be valid. 
Every existential inquiry into existential qualities as a basis for 
inference involves during its process exactly the same indeterminate 
descriptive qualification that is found in the demonstrative this. 
The only difference is that "this" has a relative minimum of 
descriptive determination. 

Another reason offered in support of the notion that purely 
demonstrative terms are merely denotative, or have no "meaning," 
proceeds from the side of descriptive terms. For there are de- 
scriptive terms which lack demonstrative reference, such as glass- 
mountain, the present king of France, etc. There is again no 



TERMS OR MEANINGS 359 



doubt as to the correctness of the fact brought forward, but 
again it does not show what it is intended to prove. No contradic- 
tion would be involved if perchance the objects referred to did 
exist. A glass-mountain might be manufactured, and there have 
been kings of France. All that descriptions not having demonstra- 
tive application show is that at a given time observation cannot 
disclose any object answering to them. What is more important is 
that such descriptions are inherent in a large number of important 
inquiries. Take, as a comparatively trivial instance, the question 
whether or not a sea-serpent exists. Obviously, investigation can- 
not proceed without some description of the term. Again, let it 
be the question of whether the ether or atoms actually exist. Un- 
less these terms have a descriptive content there is absolutely 
nothing to direct observation in the attempt to determine whether 
there are existences answering the description. Another instance 
is to be found in the case of inventions, plans and intentions prior 
to their execution, indeed at any time short of their final comple- 
tion. They are in this stage without determinate demonstrative 
reference and yet they are necessary to the operations which will 
render such demonstrative reference possible. We conclude, there- 
fore, that neither of the arguments offered gives any ground for 
modifying the position that there is a strictly conjugate relation- 
ship between generic terms (which are admitted to have meaning) 
and singular terms, whether the latter are proper names or demon- 
stratives such as this and it. 

5. Extension, Intension, and Comprehension. Traditional theory 
has held that some terms have both intension and extension, just as 
it has been held that some terms are both denotative and con- 
notative. This doctrine seems to be a hold-over from the 
Aristotelian logic. For in that system, definition is existential, 
being a grasp of the essence which determines a species. In- 
tension is then a suitable name for the definition, while the species 
determined by the definition has extension. After abandonment 
of the ontological basis of this position, confusion was introduced 
into logical doctrine by identifying extension with denotation, 
and intension with connotation in disregard of the basic considera- 
tion, viz., whether the terms involved are existential or conceptual. 
The confusion is increased and in practice supported by (1) the 



360 PROPOSITIONS AND TERMS 



ambivalence of the word object, which has the signification both 
of existential things and of strictly conceptual and mathematical 
entities, and by (2) failure to distinguish between designation and 
denotation. Combination of the two confusions is found in such 
a sentence as the following: "Conic sections connote certain 
characters or attributes and denote all the objects that have these 
characters. The objects denoted by conic sections are the mem- 
bers of the class conic sections." In such a statement, object means 
non-existential entities. The fact that only existences can be de- 
noted is ignored, the ignoring being covered up by using denoting 
as a synonym for designating. Any intelligible word designates 
something; otherwise it is a mere combination of sounds or visible 
marks, not a word at all. Xypurt, for example, designates nothing 
whatever in the English language. It is not a word. Denotative or 
existential terms and attributive or conceptual words are alike in 
designating something: they both have signification, for the mean- 
ing of words used can be understood. The important logical 
matter is the difference in what is designated. 2 

Modern logicians recognize the difference in logical form be- 
tween a singular affirmed to be one of a kind and kinds as related 
members of a more extensive kind. They accordingly recognize 
that difficulties arise when the extension of a term is said to cover 
both of these cases. They have, however, been unwilling to admit 
that the "difficulties" in question amount to violation of logical 
integrity, and hence they still go on speaking of the range of singu- 
lar objects denoted as the extension of a term. Thus in the case of a 
ship, it is said that its extension is that of all objects, past, present 
and future, to which the term ship applies. This conclusion both 
follows from and perpetuates the identification of denotation and 
extension. Logically, it gives the same force or form to a singular 
and to a kind, since various kinds of ships (sloops, schooners, 
steamboats, war vessels) are also said to be the extension of the 
term: this in spite of explicit recognition, in another connection, of 

2 The distinction made earlier between signifying and meaning is at least a 
help in avoiding confusion. The meaning of words and symbols is different 
from the signifying power of the existential things that are designated by the 
words, and only words that have existential meaning in the sense of intent or 
reference are denotative, while all words are designative, or are "names" of 
either existential or conceptual subject matter. 



TERMS OR MEANINGS 361 



the difference between the propositions, say, Hitler is a Nazi and 
Italians (or Germans) are Fascists. 

Aside from confusion in logical theory, the confusion is ma- 
terially important. For were the genuine difference consistently 
recognized, it would compel recognition that (1) extension is a 
property of some denotative terms (namely those terms that refer 
to kinds instead of to singulars); that (2) denotation and ex- 
tension are not two names for the same logical form or function, 
and that (3) non-conceptual terms have neither denotation (al- 
though they designate) nor extension. The extension of ship is 
simply and strictly the kinds of ships that exist or have existed or 
will exist; it is not singular ships, although the latter are denoted by 
ship. The definition of ship, or being of the ship-character, on the 
other hand, has no extension. The definition permits of different 
ways of being that union of interrelated characters which define 
ship. But these different ways are not the characteristic properties 
of different kinds of ships. The example is perhaps not well 
chosen since there is no abstract term, shipness, in use. Let us 
then take a mathematical term as such. Conic sections are circles, 
ellipses, parabolas and hyperbolas. As a linguistic expression, the 
sentence is grammatically of the same form as one about kinds of 
ships, flowers, metals or any existential kind. But as mathematical 
terms, the words have non-existential force. Hence, circle, ellipse 
are not lands of conic sections, but are ways of being the abstract 
universal in question. Conic section is a multiplicative conjunction 
of the characters of conicity and sectionality; circle is circularity, 
etc. Circle, ellipse, etc. do not constitute the extension of the 
term in question, for they are the category (abstract universal) 
"conic sectionality" when that is made determinate. 

What has been said indicates the need for a distinctive word to 
designate the scope of the necessary conceptual contents of an 
abstract universal or "class" in the sense of category as distinct 
from the range of applicability of a denotative term. The use of 
the word comprehension for this purpose is arbitrary as far as the 
mere word is concerned. It is not arbitrary as far as a distinct 
logical form, demanding some word by which to designate it, is 
concerned. Right-angled, scalene and isosceles constitute, con- 
junctively and disjunctively, the logical scope or comprehension of 



362 PROPOSITIONS AND TERMS 

triangularity. Such comprehension is necessary and therefore 
must be differentiated from the contingency of extension of kinds. 3 

It is not necessary to say much in addition about intension. It is 
now used in at least three ways: To designate "meaning" in the 
sense (1) of the signification of words of whatever logical form 
words may be; (2) as a synonym for the set of characteristics con- 
stituting the descriptive force of a denotative term; and (3) as a 
synonym for the logical import of a connotative or attributive 
abstract term. It is an arbitrary matter to which of the three uses 
the application of the word intension is confined in a given context. 
But in the interests of logical consistency it is far from being 
arbitrary that it be restricted to one, and only one, application in 
the same treatise. There are available the symmetrical terms 
connotation (attribution) and comprehension with respect to 
universals. Hence the use of intension to pair with extension in 
the case of denotative terms is suggested by linguistic symmetry, 
and also by the fact that otherwise there is no distinctive term to 
designate the differential kind of meaning which belongs in- 
trinsically to denotative terms; namely, a set of conjoined traits 
employed to describe a kind. In any case, some linguistic device is 
required to avoid the ambiguity otherwise attached to the word 
meaning, and to differentiate the characteristic logical forms, of 
description and definition. The two pairs, extension and intension 
for use in connection with denotative terms — and comprehension 
and definition (for use in connection with connotative terms) 
meet the needs of clarity and completeness. 

6. Collective Terms. The ambiguous nature of the word "col- 
lection" has been pointed out in discussion of the quantitative 
phase of propositions. Collection is applied indifferently to an 
indefinite aggregate of units, illustrated by a heap or pile; to a 
group of units limited by description, as a regiment, and to a 
qualitative whole in which the characteristics of units comprised 
are modified by the whole of which they are parts — as when it is 
affirmed, "The first regiment of New York fought bravely at the 
battle of Chateau Thierry," in which it is not necessarily involved 

3 Cf. the earlier remarks about circles and brackets as modes of symbolization 
of two logical forms; ante } pp. 306-7. 



TERMS OR MEANINGS 363 

that every individual soldier was brave. The old puzzles about the 
last straw which broke the camel's back, or the particular hair by- 
losing which a man becomes bald, are further illustrations of a 
qualitative meaning. 

The subject of collective terms is of special importance in re- 
lation to the general position that is taken for two reasons. One 
concerns certain difficulties which have arisen in the logic of 
mathematics. It is said, for example that numbers form an infinite 
collection in the sense of aggregate. This notion tends to as- 
similate numbers to existential objects to which the word collec- 
tion is usually applied and in the case of which units are theoreti- 
cally capable of enumeration. Puzzles then arise which would 
not arise if it were recognized that number (being number, as 
distinct from a number) is an operative formula for determining 
aggregates and collections, but it is not itself a finite collection, nor 
an infinite aggregate. Even if it be necessary to define number in 
such a way as to permit or prescribe an infinite aggregate as a mode 
or way of being number, it follows in no way that number as 
defined is itself any kind of a collection or aggregate. 

The second reason is connected with certain alleged paradoxes. 
There is the example of the "self -representative series." The map 
of England is said to constitute a reflexive serial collection. A map 
is drawn of England. It is asserted that in order to be complete 
the map must itself include the map drawn, a condition which re- 
quires drawing another map and so on in a non-terminating collec- 
tion of maps. But drawing the map is an existential operation. As 
such it takes place at a given date. There is nothing in the act of 
drawing or in its product to require the drawing of another map. 
If, for some practical, non-logical reason, it is desirable to draw 
another map of England on which the old map is represented, that 
action is another temporal occurrence. The supposed paradox 
arises only when there is a shift from the existential to the concep- 
tual. When, the phrase "drawing a map" stands for something 
purely conceptual, or a mode of operation, it is a definition or a 
formula for an operation to be executed. In this case the number 
of maps to be drawn and the objects they are to be maps of are inde- 
terminate as far as the conception is concerned. A map or a collec- 



364 PROPOSITIONS AND TERMS 

tion of maps thus depends upon conditions and operations that are 
existential in nature and hence are not "implied" by the concep- 
tion. 

There is also the alleged paradox in the case of the soldier barber 
who is ordered by his superior office to shave all the men and only 
the men in his company who do not shave themselves. It is then 
asked, is the barber himself comprised in the collection of men to 
be shaved? If he is one who does belong in the collection of those 
who do not shave themselves, he disobeys the order if he does 
not shave himself. In case, however, he obeys the order and does 
shave himself, he is one who shaves himself, and hence equally 
disobeys the order. The appearance of contradiction vanishes the 
moment reference to time and date is introduced, and since the act 
of shaving a given person is existential, such a reference must be 
introduced implicitly in the context or else explicitly. When the 
act of shaving is interpreted existentially and temporally, the com- 
mand is unambiguous and there is no difficulty in determining how 
it is to be obeyed. If the barber is one who has not in the past 
shaved himself, then he obeys the order by now shaving himself; 
if he has shaved in the past, he obeys the order by nonj) abstaining 
from shaving himself.* The contradiction alleged to exist arises 
only when the existential and the conceptual are confusedly 
identified. 

So-called reflexives are said to involve a self -representative and 
hence non-terminating collection. Similar analysis applies. Take, 
for example, such seemingly reflexive relations as "love of love," 
"hate of hate." The love and hate forming the first member of 
each pair are concrete nouns, having existential reference. They 
designate acts performed at some time or place, whether once or 
repeatedly. The love and hate which are second members of the 
paired terms are of a different form. They are identifiable with 
the first terms members only verbally. For they designate abstract 
characters, which, of course, are conceptual, not existential. 
Change the wording to read "love of benevolence" and "hatred of 
malevolence" and any shadow of a reflexive relation and of a self- 

_ *Cf. P. W. Bridgman, Scripta Mathematics ■, Vol. II, p. 113. The interpreta- 
tion given above is not identical with that of Bridgman but he shows clearly 
that the temporal quality of acts of shaving is the reason there is no paradox. 



TERMS OR MEANINGS 365 

representative collection disappears. "Hating" is a concrete act; 
"hate" as the object of the act is abstract. 

A collection is distinguished in form from both a kind and from 
a class in the sense of category. A dictionary is, from one point of 
view, a collection of words. At a given place and time, the number 
of words is definitely enumerable, although a dictionary may exhibit 
increase or decrease in the number of words forming the collection 
in subsequent or former editions. Like a postage stamp collection, it 
is capable of variation in number at different times, but at a given 
time it has just the number of units which it does have. The generic 
terms applying to a kind of objects, applies to all of an indefinite 
number of objects marked by specified characteristics, but while 
it is indefinite, instead of definite, in the number of singulars to 
which it refers, it is ideally completely determinate as to the set of 
characteristics it denotes. A category is constituted by the interre- 
lation of two abstract universals, each of which may be complex. 
Hence, once more, number is not a collection but is a formula for 
operatively determining collections, while a number, 2 or 1700, is a 
collection satisfying the conditions prescribed by the definition of 
number. The collection, however, is not a collection of objects or 
existential singulars but is a collection of operations: namely, the 
operations which determine, according to the definition of number 
in the abstract, units. Thus 2 means that the operation which 
constitutes 1 is performed twice. 

7. T articular Terms. The word "particular" is ambivalent. It is 
sometimes a synonym for "certain" in its sense of definitely 
specified, as in the phrase "the particular man of whom you are 
speaking." In this usage, "particular" is a synonym for "singular," 
and there is nothing further to be said of its logical meaning. The 
logical force of "particular" as distinct from singular, is found when 
the word is applied to existential materials which have not as yet 
been ordered with respect to their status as evidential data. At an 
early stage of inquiry, there may be an accumulation of observed 
materials whose relevancy and force in respect to the problem in 
hand is uncertain. They are fragmentary and partial, and in this 
capacity are particular. As a rule, the plural form "particulars" 
designates possible data while the word "particular" designates a 
specified determinate existential subject-matter. 



366 PROPOSITIONS AND TERMS 

I return, in closing, to a point already discussed, now taking 
it up in its wider theoretical bearings. There is a controversy as to 
the intension of singular terms. Mill, as we have seen, holds that 
proper names have no "meaning," while other logicians hold that 
demonstratives have no meaning except as expressly qualified by a 
descriptive term. Jevons, on the other hand, says "Logicians have 
erroneously asserted that singular terms are devoid of meaning in 
intension, the fact being that they exceed all other terms in that 
kind of meaning." 4 

With respect to Mill's contrary position, we may cite in addition 
to what has already been quoted, his statement that proper names, 
like the mark made by the robber in the story Arabian Nights, 
are "simply marks used to enable individuals to be made subjects of 
discourse." If a word is understood simply in the sense of sounds 
or visible marks employed, then it is true of any word that it is 
either "simply a mark used" to enable something, whether a singular 
or a kind, to be used as a subject of inquiry, or else an indicator of 
something to be said about them during the course of inquiry — the 
latter being the case in words which designate conceptual material. 
But as a word or symbol, every word has the meaning, either in 
intension or comprehension, of that which it stands for — its 
referent. That an existential term, denoting a singular, enables that 
for which it stands to be a subject of discourse and inquiry, is 
possible only because it already has some differentiated and dif- 
ferential intension; otherwise it would be so completely indetermi- 
nate that it could not identify and mark out anything in such a way 
that the latter could be the subject of one mode of discourse or one 
inquiry in distinction from thousands or millions of other predica- 
tions that would be possible. When Mill admits that a "mark" has 
a special intent he admits in effect what he denies in words. 

It follows that Jevons' position is the only one that can be taken. 
What is demonstratively denoted by a proper name is inexhaustible 
in its meaning or intension, instead of being lacking in all such 
meaning. Take London, England, for example, as a conventional 
mark enabling a singular object to be the subject of discourse and 
inquiry. Its meaning in intension is first of all topographical, but it 
extends far beyond physical location and area. Its meaning in in- 

4 W. S. Jevons, Principles of Science, p. 27. 



TERMS OR MEANINGS 367 

tension is historic, political, cultural; it includes a past, a present and 
potentialities not yet realized. What is true of its intension is that 
it cannot be completely circumscribed at any given time by any set 
of descriptive qualifications; i.e., its meaning in intension is inex- 
haustible. The same statement holds in principle of any singular 
term, for such a term denotes a spatio-temporal career. 

The wide theoretical bearings that were mentioned render the 
particular point at issue a critical one for logical doctrine. It links 
up with the view that the subject-matter of the logical subject of 
judgment is a discriminated determination of certain elements 
within a larger qualitative situation, the material in question being 
selected to describe a problem and to provide conditions which test 
any proposed solution. Secondly, it links up also with the doctrine 
that singulars and kinds are determined in correspondence with 
each other, there being no singular which is not of some kind (or 
having characteristics which descriptively determine a kind), and 
no kind which is not ultimately a kind of existential singulars. 
Thirdly, it is consistent with the denial of atomic particulars and 
atomic propositions. For the ultimate ground of belief in atomic 
terms and propositions is the idea that demonstratives lack all 
descriptive qualification. It also discloses the gratuitous nature of 
that doctrine of names which holds that in an ideal language every 
singular would have its own unique name standing in one-one 
correspondence with it. It also points to the fallacy in the doctrine 
that while the conception of kinds and of generic propositions has a 
place in logical theory, the theory about the latter should be so 
formal as to provide no place for concrete existential subject- 
matters. Current logical formalism in logic claims to be allied ex- 
clusively with non-existential propositions such as are exemplified in 
mathematics, while at the same time it recognizes propositions of 
existential import, covering up the inconsistency by confusing the 
two modes of the general, the generic and the universal. 



Part Four 

THE LOGIC OF SCIENTIFIC METHOD 



CHAPTER XIX 

LOGIC AND NATURAL SCIENCE: 
FORM AND MATTER 



It is commonplace that logic is concerned in some sense with 
form rather than with matter. Such words as "and, or, any, 
only, none, all, if, then, is and is not" are not material con- 
stituents of propositions. They express ways in which material is 
arranged for logical purposes, no matter how "logical" is defined. 
Such sentences as "John loved Mary" and "Peter disliked Joan" 
have the same form but different material contents, while "Two 
plus two equals four," and "The sum of three interior angles of a 
triangle equal two right angles" are of the same form in spite of the 
difference of material content. 1 Again, the proposition "Carnegie is 
wealthy" and "Millionaires are wealthy" are of different forms, 
since the first proposition is about a singular as one of a kind, and 
the other is about a relation of kinds. 

The intrinsic place of form in logical subject-matter is more than 
a commonplace. It states the character which marks off logical 
subject-matter from that of other sciences. It provides the funda- 
mental postulate of logical theory. Recognition of this fact does 
not, however, settle the question of what the relation of form and 
matter is; whether there is any relation, what it is, or whether there is 
complete absence of relation. This problem is so fundamental that 
the way in which it is dealt with constitutes the basic ground of 
difference among logical theories. Those which hold there is no 
relation between form and matter are formalist^. They differ 
among themselves; some hold the doctrine that forms constitute a 
realm of metaphysical possibilities; others that forms are syntactical 

1 "Material" as used in the connection above is not to Jbe identified with 
existentially material. Conceptual subject-matter is material in a non-existential 
proposition. 

371 



372 THE LOGIC OF SCIENTIFIC METHOD 

relations of words in sentences. The opposed type of logical theory 
holds that forms are forms- of -matter. The differential trait of the 
variety of this type of theory expounded in this book is that logical 
forms accrue to subject-matter in virtue of subjection of the latter in 
inquiry to the conditions determined by its end — institution of a 
warranted conclusion. 

1. Introduction. There is no need to repeat or summarize here 
the arguments that have been adduced in support of this position. 
It is pertinent, however, to repeat, with some expansion, a point 
earlier made; namely, that the idea in question (that forms accrue to 
material which did not possess them in its original form) is a vera 
hypothesis, not a conception invented to serve the ad hoc need of 
a special logical theory. There are many instances in which original 
crude material takes on definitive form because of operations which 
order that material so that it can subserve a definite end. Indeed, 
this sort of thing happens wherever original raw materials are re- 
arranged to meet requirements imposed by use of them as means to 
consequences. The supervening of form upon matter did not await 
the rise of logic. It would be truer, on the contrary, to say that 
logic itself had to wait until various arts had instituted operations by 
means of which crude materials took on new forms to adapt them 
to the function of serving as means to consequences. 

Of the numerous illustrations which might be given, two will be 
selected as exemplary, namely, legal forms, and esthetic forms. The 
formal nature of juristic conceptions is notorious, so much so that 
many times during the history of law there has been good ground 
for complaint that forms of procedure had become the controlling 
factor at the expense of substance. In such cases, they ceased to be 
forms-of-matter and were so isolated that they became purely 
f ormalistic — a fact which perhaps contains an instructive lesson for 
logic, since it is clear that legal forms should be such as to serve the 
substantial end of providing means for settling controversies. More- 
over, the objective aim is to provide in advance, as far as possible, 
means for regulation of conduct so that controversies are not so 
likely to arise. Rules for ordering human relations, by prescribing 
the ways in which transactions should be conducted exist in order 
to avert conflicts, to settle them when they occur and to obtain 
redress for the injured party. These rules of law provide multi- 



LOGIC AND NATURAL SCIENCE 373 

farious examples of the ways in which "natural" modes of action 
take on new forms because of subjection to conditions formulated 
in the rules. As new modes of social interaction and transactions 
give rise to new conditions, and as new social conditions install 
new kinds of transactions, new forms arise to meet the social need. 
When, for example, a new type of industrial and commercial 
enterprise required large capital, the form known as limited liability 
supervened upon the forms constituting the legal rules of partner- 
ship. 

A simpler example is found in the legal form known as contract. 
Agreements between persons who combine their activities for a 
joint end in which one person promises to do something to con- 
tribute towards reaching the end and the other person agrees to do 
something else, are examples of "natural" or crude modes of action. 
Such reciprocal engagements must have arisen at an early period in 
social life. But as agreements multiplied and the problem of their 
execution became pressing, as business became less and less a matter 
of direct barter and more and more a matter of agreement to ex- 
change goods and services at a future time, certain forms arose to 
differentiate among kinds of reciprocal engagements. Some of them 
were treated as mere promises, failure to execute which brought 
no enforceable penalties, while others were such that failure to 
execute them imposed a liability upon one party and conferred an 
enforceable claim upon the other party. 

There is nothing in the mere act of promising which differen- 
tiates one kind from the other. Certain purely formal traits had 
to be added to the making of a promise in order to render it en- 
forceable; say, a seal, and evidence of a "consideration." The sum 
of these forms define a contract. But while the conception of 
contract is purely formal, it is (1) a form-of -material, and (2) it 
accrued to prior non-formalized material in order that the ends 
served by that material might be attained on a wide scale in a 
stabilized way. As commercial transactions became more com- 
plex, sub-kinds of contract arose, each kind of transaction having 
its own distinctive formal traits. 

Men did not wait for the rise of logical theory to engage in 
inquiry in order to reach conclusions, any more than they waited 
for the law of contracts to make reciprocal promises. But experi- 



374 THE LOGIC OF SCIENTIFIC METHOD 

ence in inquiry, as in conduct of business transactions, made it 
evident that the purpose for which inquiry is carried on cannot be 
fulfilled on a wide scale or in an ordered way except as its ma- 
terials are subject to conditions which impose formal properties on 
the materials. When these conditions are abstracted, they form 
the subject-matter of logic. But they do not thereby cease to be, 
in their own reference and function, forms-of -subject-matter. 

That the objects of the fine arts, of painting, music, architecture, 
poetry, the drama, etc., are what they are as esthetic objects in 
virtue of forms assumed by antecedent crude materials is too ob- 
vious for argument. No one acquainted with the material is at any 
loss to distinguish between Doric and Gothic forms in architecture 
or between symphonic and jazz forms in the arrangement of tonal 
material. Similarly, in respect to land, there are forms of record, 
etc., that have to be conformed to in order to give ownership a 
legal status. No one has any doubt about the difference between 
this sort of form with respect to land and that which makes a 
landscape an esthetic object. Poetry is marked off from prosaic 
description by some special form. That its material existed inde- 
pendently of and prior to artistic treatment, and that the relations 
by which that material takes on esthetic form (rhythm and symme- 
try for example) also exist independently, is undeniable. But it re- 
quires the deliberate effort which constitutes art, and the deliberate 
efforts constituting various arts, to bring the antecedent natural 
materials and relations together in the way that forms a work of 
art. The forms that result are capable of abstraction. As such 
they are the subject-matter of esthetic theory. But no one could 
construct a work of art out of the forms in isolation. Esthetic 
forms very definitely accrue to material in so far as materials are 
re-shaped to serve a definite purpose. 2 

2. The Failure of Formalism. The issue of strict logical for- 
malism, of any theory which postulates forms apart from mat- 
ter of logical forms versus forms-of-matter, comes to a head in the 
question of the relation to method in the natural sciences. For if 
f ormalistic logic is unable to deal with the characteristics of scien- 
tific method, a strong, if indirect, confirmation of the position 

*What I have said in Art and Experience, in chapter VII, on The Natural 
History of Form can be carried over, mutatis mutandis, to logical forms. 



LOGIC AND NATURAL SCIENCE 375 

taken in this volume is obtained. It would at first seem as if pure 
formalism should lead those who accept that doctrine to abstain 
entirely from any reference whatever to method in the natural 
sciences, since that method is truistically concerned with factual 
materials. Such, however, is not the case. Formalistic logic is not 
content to leave the topic of method in the existential sciences 
severely alone. Belief in some sort of connection is usually ex- 
pressed by the phrase "logic and scientific method." Another 
expression conveying the idea of connection is the phrase "ap- 
plied logic." 

Both expressions serve to beg the issue, or at least to disguise the 
fact that there is an issue. In the case of the seemingly innocent 
phrase "applied logic," the real issue is whether or not the expres- 
sion has any meaning at all when logic is defined in terms of forms 
entirely independent of matter. For the issue is precisely whether 
such forms can be applied to matter. If they cannot, applied logic 
is a meaningless term. For the question is not whether logical 
forms are applied, in the sense of being used, in inquiry into exis- 
tential subject-matter, but whether they could be so used if they 
were purely formalistic. The fact that investigation into natural 
phenomena, when it is scientifically conducted, involves mathe- 
matical propositions, certified purely formally, may be cited, for 
example, as an instance of "applied" logic. The fact is not only 
admitted, but, as has been shown in the course of previous dis- 
cussions, is necessary. The admission proves nothing, however, as 
to absence of relation between form and matter. It but raises the 
problem of the conditions under which the application or use of 
non-existential propositions in determination of propositions hav- 
ing material content and import takes place. 

It is precisely on this fundamental matter of conditions of ap- 
plication that the formalistic theory breaks down. It would seem 
to be evident in the very nature of the case that a form which is 
completely indifferent to matter is not applicable to any one 
subject-matter rather than to another, much less capable of indicat- 
ing in any selective way to what matter it shall be applied. If the 
matter in question were completely determined as formed matter 
when it is given, the problem would not arise, and it may be argued 
with a certain show of plausibility that such is the case in mathe- 



376 THE LOGIC OF SCIENTIFIC METHOD 

matics. But with respect to the subject-matter of the natural 
sciences, no such plea can be made. Either logical forms have 
nothing at all to do with it (so that the question of applicability 
does not arise) or their application is such as to introduce into, or 
cause to supervene upon, the original subject-matter those prop- 
erties which give it scientific standing. It is not easy to see how 
this supervention can take place unless logical forms are capable 
of somehow selecting just that specific subject-matter to which 
they should apply in any given scientific investigation, and are 
also capable of arranging or ordering that subject-matter so that 
conclusions of scientific validity are arrived at. For the minimum 
meaning that can be assigned to "application" in physical inquiry 
is selection (involving elimination) and arrangement. The brunt 
of the issue, moreover, is not faced until it is recognized that in 
any case the problem of what existential materials are to be se- 
lected and of how just those materials are to be ordered, is a 
differential one. For purely in the abstract, forms if they apply 
to any one subject-matter, apply equally and indifferently to all 
subject-matters, while in natural inquiries there is always the prob- 
lem of determining some special materials in some special order. 
Whatever may be thought of this general argument, it at least 
serves to define what is meant by the necessity of determining the 
conditions under which pure and empty forms are applicable. 

Discussion recurs, accordingly, to this problem. It is admitted 
that non-existential propositions, in the way of hypothetical uni- 
versal^ are necessary in order to arrive at fully grounded conclu- 
sions in natural science. This consideration is conclusive against 
traditional empiristic logic (of the type of Mill) which holds that 
a sufficient number of singular propositions will "prove" a gen- 
eralization. But refutation of this position is far from substantiat- 
ing the doctrine of the merely formal character of such proposi- 
tions as they are used in natural science. For the crux of the 
problem is how in any given case the universal propositions em- 
ployed acquire that content which is a condition of their determi- 
nate applicability. It is not enough that the propositional function 
"If Y, then X" should be seen to be a required form for reaching 
any scientifically grounded conclusions. It is necessary that Y 
should be given a determinate value such that X may also be given 



LOGIC AND NATURAL SCIENCE 377 

a determinate value. In addition, it is an acknowledged principle 
that no universal proposition "implies 5 ' singulars, so that in any 
case there is no direct transition from universal to existential 
propositions. Suppose, for example, that, in some unexplained 
way, the purely formal "If Y, then X" has acquired content, as in 
the following: "If anything is human, then it is mortal." It is 
one thing to hold that such a proposition has directive force in 
instituting operations of controlled observation that determine 
whether any existing object has the characteristic traits describing 
the kind "human" from which it may be warrantably inferred that 
anything of this kind is "mortal." But logically it is a very differ- 
ent thing to hold that, apart from its operational function in 
instituting controlled observation, it is applicable to existence. In 
short, we are brought to the conclusion that application is a mat- 
ter of existential operations executed upon existential materials, so 
that in the natural sciences at least, a universal proposition has a 
purely functional status and form. 

In the above illustration, it was assumed that somehow or other 
the purely formal propositional function "If Y, then X," has ac- 
quired some content so that Y has the meaning "human" neces- 
sarily related to the value "mortal." It is evident without argument 
that unless definite values are "insertible," the formal propositional 
functions have no application even operationally to any one exis- 
tential subject-matter rather than to another. In what way then 
are these special values given to X and Y? Why in a specific in- 
quiry can we not substitute the values that would give the proposi- 
tion "If angelic, then mortal"? Or, "If diseased, then immortal"? 
Such illustrations, capable of indefinite multiplication, make it 
clear that the necessary relation in question is one of contents hav- 
ing a certain form, not one of mere forms apart from content. 
The question recurs with added force: How can pure forms ac- 
quire related contents? What are the logical conditions under 
which they acquire those contents without which the application 
to existence, that marks inquiry in the natural sciences, is impos- 
sible? 

Suppose that somehow the propositional form u y0x" (or yRx) 
has in some unspecified way gained enough content so that it is 
expressed as "x is assassinated." Ignoring the problem of how the 



378 THE LOGIC OF SCIENTIFIC METHOD 

material content "assassinated" was introduced, the question still 
remains why one value rather than any other of an indefinite num- 
ber of possible values is given to x. It is doubtless a matter of 
common knowledge that Julius Caesar and Presidents Lincoln and 
Garfield were assassinated, and that Cromwell and George Wash- 
ington were not. But how did it become a matter of public in- 
formation? It would be absurd to say that it became such because 
of the form of the propositional function. The alternative is the 
obvious one that it was established by observation and record. 
The conception of "assassination," exclusively distinct from other 
modes of dying, is necessarily involved. Logically, the disjunc- 
tive form just noted, and the hypothetical proposition "If such 
and such differential characteristics, then this specific kind, assassi- 
nation" are logically necessary. But they are conditions to be 
satisfied, not inherent properties; and they can only be satisfied by 
means of extensive and complex existential operations performed 
upon existential materials. 

The assumption that pure forms constitute the required applica- 
tion is one more instance of confusion of the functional and direc- 
tive force of a formal logical relation in prescribing conditions to 
be satisfied with an intrinsic structural property. Take the ex- 
ample frequently used in contemporary logical texts, "X is mortal," 
which, it is said, becomes a proposition when Socrates is "substi- 
tuted" for X. Now either "Socrates" is here an empty symbol, 
devoid of content and reference, or (1) it has meaning and (2) that 
meaning is such as to be existentially applicable. If it is a formal 
symbol, nothing is gained by substituting it for X. If it has mean- 
ing in application, the meaning does not follow from the proposi- 
tional function save by means of observations and observable records 
which determine (1) that an object, Socrates exists (or has existed 
at some definite place-time) and (2) that this object possessed the 
characteristics describing the kind men. 

The propositional function "X is man" is then an expression of 
highly equivocal form. As soon as it is stated in its proper form 
(as a hypothetical universal), it is evident that operations indicated 
by the formula as a rule for something to be done, are necessary 
to determine the existence of an object satisfying the conditions 
laid down in the function. "X is human," in other words, formu- 



LOGIC AND NATURAL SCIENCE 379 

lates a problem: — that of discovering the object or objects that 
are such as to possess the properties prescribed by the term "hu- 
man" — a condition which requires that the meaning of "human" 
be already determinate. It follows that existential "application" 
necessarily (1) involves an existential problem with reference to 
which the contents of the non-existential propositions have been 
selected and ordered, and (2) the operational use of the formally 
non-existential proposition as a means of observational search for 
objects that satisfy the conditions it prescribes. 

It is pertinent to repeat in this context the point which has been 
repeatedly made about doctrinal confusion of the two forms of the 
general proposition, namely the generic and the universal. For 
this confusion is absolutely indispensable for direct passage from 
universal propositions to propositions about a singular as of a kind 
and to propositions about a relation of kinds. The usual line of 
reasoning in support of the confusion runs about as follows: A 
general proposition (in the sense of generic) such as "All men are 
mortal," in the sense that "Each and every man who has ever 
lived, who is now living or who will ever live, has died or will 
die" (evidently a proposition of existential import) is said, quite 
correctly, not to refer to any specific singular but to any one of an 
indefinite number of singulars, the existential range of which in- 
cludes many singulars not now capable of observation. It affirms, 
in other words, a connection between the set of traits which de- 
scribes mankind and the set of traits which describes the kind 
mortal; or those subject to the occurrence of the event, dying. It 
is also affirmed (correctly) that ultimately the warrant for assert- 
ing this connection is a proposition which affirms that the charac- 
ters "being human" and "being mortal" are necessarily interrelated. 
Short of such a proposition, the proposition in its existential force 
is at best a generalization, in the sense of an extension, of what has 
been observed in some cases to an indefinite number of unobserved 
cases. Such an extension is "empirically" confirmed by observa- 
tion of a large number of events actually occurring. But it is, in 
theory, open to nullification as a generalization at any time, as 
much so as is the proposition "All swans are white." What takes 
the proposition out of this precarious form is, as a matter of fact, 
biological and physiological investigations which indicate a neces- 



380 THE LOGIC OF SCIENTIFIC METHOD ^ 

sary interrelation between the characters that define "living" and 
those which define "dying"— as conceptual structures. 

So far there is no confusion. But the fact that the proposition 
"All men are mortal" does not refer to any specified singular as 
such, or to any one man rather than to any other, is illegitimately 
interpreted to mean that it does not refer to any singular whatever. 
The proposition is then converted into the non-existential proposi- 
tion, "// human, then mortal" The conversion is illegitimate be- 
cause it is one thing, logically, to make propositions about traits 
or characteristics which describe a kind in "abstraction" from any 
given singular of the kind, and a radically different thing to make 
a proposition about abstractions qua abstract. The absence of 
specific reference to one singular rather than another is no ground 
for a proposition free from any existential reference. There is no 
logical road from "No specific singular" to "No singular what- 
ever" in the sense of abstraction from existential reference as such. 
Yet this is the impossible road taken by logical doctrine when it 
assimilates the form of generic propositions to those of universals. 

The fact that in the context of discussion of logical forms it is 
expressly pointed out that singular and generic propositions — all 
propositions of the / and O form — have existential reference, while 
no universal of the A or E form has existential reference, shows 
that the confusion in question is not an accidental slip, or a case of 
occasional carelessness. The confusion is inherently essential to 
any doctrine which (1) holds that logical forms are formal in the 
sense of being independent of content, factual or conceptual, and 
yet (2) are capable of material application — as is inherently in- 
volved in the methods of the natural sciences if the latter have any 
connection at all with logic. In spite of the appearance of the 
word all in the proposition "All men are mortal" (as a proposition 
referring to each and every singular of the kind described by the 
sets of distinguishing traits that determine respectively the kinds 
"human beings" and "subject to death"), the proposition is logi- 
cally an / proposition — a fact recognized in the doctrine expressly 
stated (in another context) that / and O propositions alone refer 
to existence. 3 

3 A conspicuous case of the confusion in question is found in the treatment of 
the null class. That the kinds Indian Popes, Emperors of the United States, 



LOGIC AND NATURAL SCIENCE 381. 

I recur to the earlier statement that while scientific method 
is not possible without non-existential if-then propositions, and 
while such propositions are necessary conditions of scientific 
method, they are not its sufficient conditions. An hypothesis con- 
cerns what is possible, and a proposition regarding possibles is in- 
dispensable in inquiry that has scientific standing. The hypothesis 
is formulated in an abstract if-then proposition. It then formu- 
lates a rule and method of experimental observation. Conse- 
quences of the execution of the indicated operations define 
application in the only logically coherent sense of that conception. 
One indispensable condition of application in the case of method 
in natural science is, therefore, that the contents of the hypotheti- 
cal proposition be themselves determined by prior existential in- 
quiries in such a way that the contents are capable of directing 
further operations of observation. Moreover, even in such cases, 
the fallacy of affirming the antecedent because the consequent is 
afErmed is committed, unless independent operations of extensive 
observation have affected the afErmed relation of contents with a 
probability coefficient. The validity of any such coefficient is 
conditioned upon the nature of other existential propositions and 
their material consequences. 

The case of ordered discourse in which all propositions are, as 
such, non-existential in import, and which form a series in virtue 
of the implicatory, as distinct from the inferential, function affords 
at best but a seeming exception to the principle that forms are 
forms-of -matter. For the sequential order of any such series is 
determined in all cases, in which the final proposition has ap- 
plicability, by material conditions. Theoretically or in the ab- 

have no members, and are instances of a "null class" is a statement having 
radically different logical form from expressions like, say, circular-square, or 
vicious-virtue. The first is an instance of contingency; up to a given date, no 
such singular has existed or, if it has existed, has not been observed. The second 
set of examples express necessary exclusion of an instance, since the related 
conceptions contradict each other. The case of vicious-virtue is perhaps es- 
pecially instructive. There can be no doubt that there occur actions which 
conventionally are called virtuous but which, from the standpoint of some 
ethical theories, are inherendy vicious and vice versa. This fact does not 
signify that the definitions of vice and virtue are compatible with each other, 
but that from the standpoint of one ethical theory the definitions of vice and 
virtue held by its adherents are incompatible with the conceptions held by ad-J 
herents of another ethical theory. 



382 THE LOGIC OF SCIENTIFIC METHOD 

stract, an indefinite variety of series of implicatory propositions is 
possible— as in mathematics. But— as appears in mathematical 
physics— mathematical implicatory series, in all instances in which 
applicability enters as a condition, have their contents and their 
order (in determining a final hypothetical proposition) controlled 
by the observed existential conditions that form the problem re- 
quiring a generalized solution. Otherwise, contents would be 
taken and ordered in such an indeterminate way that even if the 
order were necessary with respect to rigor of implication, there 
would be no assurance whatever of any kind of final applicability. 
We are again forced to the conclusion that formal relations state 
conditions to be materially satisfied. 

The arguments adduced show incontestably that pure forms, 
where "pure" means "completely independent of relation to 
meaning-contents" (factual and conceptual) cannot possibly de- 
termine application in the sense in which application is necessary 
in the natural sciences. There is one especial instance frequently 
given in recent logical treatises which is supposed to prove that a 
universal proposition is capable of direct determination of an in- 
ference regarding existential matters. It is, accordingly, worth 
examining, since this will disclose the typical fallacy involved in 
all instances of the doctrine in question. The example referred 
to is the following: From the if-then proposition "If there are 
more inhabitants in a town than there are hairs on the head of any 
inhabitant of that town, then some two (or more) inhabitants 
have the same number of hairs on their heads." There is, of course, 
no possible doubt that if the conditions stated in the antecedent 
clause are satisfied, then the state of affairs set forth in the conse- 
quent clause will follow. But as far as an existential proposition 
about a person or persons in any actual town are concerned, the 
proposition only raises a question: Are the conditions satisfied? 

This question is one of material fact. It can be answered only 
by independent operations of observation that are directed by the if- 
then proposition in question. This proposition, when so employed, 
renders it unnecessary to count the hairs on the head of every 
person in a town. It is necessary only to have a dependable esti- 
mate of the number of hairs on the head of the bushiest-haired 
person that can be found and also have a dependable estimate of 



LOGIC AND NATURAL SCIENCE 383 



the number of inhabitants of the town. Given these existential 
data, the inferred proposition that some two persons do (or do 
not) have the same number of hairs on their heads will be war- 
ranted. The conclusion that they do not have, would be more 
likely in the case of a hamlet where there are only a few in- 
habitants. Observational data would suffice in the case of a very 
large city like London or New York to warrant the existential 
proposition that two or more (unspecified) persons do have the 
same number of hairs on their heads. But it would do so not be- 
cause that proposition is "implied" by the hypothetical proposi- 
tion in question, but because of determination by observations of 
existential data, taken in connection with the hypothetical proposi- 
tion as the rule for their selection and ordering. 

A similar mixing of propositions of two different logical forms 
is found in the notorious case of Epimenides and Cretans as liars. 
Epimenides who is a Cretan, according to an existential proposi- 
tion, affirms that "All Cretans are liars." Hence, it is argued, a 
contradiction or "paradox" inevitably arises. Unless Epimenides 
speaks the truth, it does not follow that All Cretans are liars, and 
if he speaks the truth, then the proposition follows that "Some Cre- 
tans tell the truth" and hence the proposition that "All Cretans 
are liars" is false. Only a little analysis is required to show that 
if the proposition "All Cretans are liars" is a generic proposition, 
meaning that a disposition to lie is one of the characteristic traits that 
mark off Cretans as a kind from other kinds of Greeks (or of human 
beings) , it does not follow that every Cretan is necessarily a liar and 
that he always lies. For the trait of lying describes a Cretan only 
in conjunction with other circumstantial, or temporo-spatial, con- 
ditions which are contingent since they are existential. In other 
words, if the proposition is generic, some Cretan may sometimes 
tell the truth, and there is no contradiction. On the other hand, 
if the ambiguous term "all" is interpreted in the sense of a neces- 
sary relation between being a Cretan and being a liar, or as the 
contents of a universal, instead of a generic, proposition, it poses a 
question as far as any existential proposition is concerned. If 
Epimenides tells the truth when he says "All Cretans are liars" 
then by definition he is not in fact a Cretan. For denying the 
consequent denies the antecedent. If on the other hand, it is 



384 THE LOGIC OF SCIENTIFIC METHOD 

found, by adequate observation of existential data, that he is lying 
then it is necessary to revise the hypothetical universal proposition 
in question— a state of affairs that always occurs when application 
of a universal proposition to existential condition is found to yield 
data that are not in accord with the requirements of the universal. 
The conclusion of the analysis is that only a mixing of the two 
forms, the generic and the universal, produces the alleged contra- 
diction. 4 

Exactly the same analysis applies to the existential conclusion 
that in a country having a monogamous system, it can be inferred 
that the number of husbands and wives is equal without having to 
go through the tedious process of enumeration of the actual num- 
ber of husbands and wives. For independent operations of ob- 
servation are required to determine whether a given country has 
or has not a monogamous system. The same holds in the case of 
the inference that in a given hall the number of seats and the num- 
ber of persons may be determined to be equal without counting 
the number of either. For again, it requires independent observa- 
tion to determine that every seat is in fact occupied. The source 
of fallacy in all these instances is that, first, cases are taken 
whose materials have been prepared by prior existential operation, 
and, secondly, that the way in which they were prepared is ig- 
nored, the ignoring being here equivalent to denial. 

The discussion, so far, has supported the doctrine that logical 
forms are forms-of-matter on a negative ground: namely, the 
contradictions that exist upon the alternative basis. The positive 
support of the doctrine is the fact that in scientific inquiry, specific 
contents, factual or conceptual, as well as forms in which they 
are ordered, are determined in strict correspondence with each 
other. An attempt to justify this statement at this juncture would 
be to repeat the analyses and conclusions of the whole two pre- 
vious Parts. Instead of engaging in this superfluous task, the point 
of issue will be approached by consideration of the principle that 
is present in analogous subject-matters. The basic category of 

4 A similar analysis applies to the alleged paradox of the "autological" and the 
"heterological." In one set of propositions, the words have to do with a con- 
ception or a category and in the other case with a word, which is existential. 
These "paradoxes" occur only when the logical ambiguity of "class" (as meaning 
both kind and category) is taken advantage of. 



LOGIC AND NATURAL SCIENCE 385 

logic is order. It is also the basic category of all the arts. The 
universal order of material contents in every intelligently directed 
procedure is that of means-to-consequences; actual existential ma^ 
terials providing the "stuff," while the status of the material as 
means requires operations of selection and of re-arrangement so 
that special interactions may be instituted to effect the conse- 
quences intended. At the outset, when a certain result is desired, 
some existing material in its "natural" or crude state may be used 
— as a stick conveniently at hand is used to pry a stone. In such 
a case, required operations of observation are directed merely to 
selection of a suitable stick. But when need for a certain kind 
of consequence is recurrent, it becomes advisable to select just the 
materials that lend themselves to formation of the tools that most 
expeditiously and economically effect the intended end in a great 
variety of temporal-spatial circumstances. Materials are then se- 
lected and shaped to be levers. At a certain level of culture, the 
lever may be simply a crowbar. But as need develops that con- 
sequences be brought about in a widened variety of circumstances, 
the principle of leverage is expanded and refined to include a 
variety of physical devices, which, scientifically stated, avail them- 
selves of the law of momenta to obtain mechanical "advantage." 
An expert mechanic thus becomes acquainted, even apart from 
comprehension of a scientifically formulated law, with a variety 
of contrivances all of which are levers because, in spite of their 
different sizes and shapes, they have the functional relation of be- 
ing means to a specified distinctive kind of consequence. 

Every tool, appliance, article of furniture and furnishings, of 
clothing, every device for transportation and communication, thus 
exemplifies practically and existentially the transformation of crude 
materials into intentionally selected and ordered means so that 
they are formed-matter; or, stated from the side of form, so that 
there are forms-of -matter. Form and matter may become so in- 
tegrally related to one another that a chair seems to be a chair and 
a hammer a hammer, in the same sense in which a stone is a stone 
and a tree is a tree. The instance is then similar to that of the 
cases in which prior inquiries have so standardized meanings that 
the form is taken to be inherent in matter apart from the function 
of the latter; or (as in the case of some of the formalistic argu- 



386 THE LOGIC OF SCIENTIFIC METHOD 

ments which have been criticized) matter is treated as if it were 
itself purely formal— a conclusion drawn because integration of 
form and matter is so completely accomplished. 

These instances exemplify the principle stated in the first part 
of this chapter; namely, that forms regularly accrue to matter in 
virtue of the adaptation of materials and operations to one another 
in the service of specified ends. They are here brought forward, 
however, for a different but related purpose — namely, to illustrate 
the principle that in all cases of f ormed-materials, form and matter 
are instituted, develop and function in strict correspondence with 
each other. Every tool (using the word broadly to include every 
appliance and device instituted and used to effect consequences) is 
strictly relational, the relational form being that of means-to- 
consequences, while anything which serves as effective means has 
physical existence of some sort. 

1. The abstract relation of means-consequence may be formally 
analyzed. It involves correspondence of material and procedural 
means, a correspondence illustrated, in the field of tools, utensils, 
articles of dress, etc., in the fact that materials and techniques are 
reciprocally adapted to each other. Technical processes of reshap- 
ing raw materials are invented so that they are capable of reshaping 
the crude material to which they are applied to make the latter 
function as means. The processes must be such as to be capable of 
just those modes of application that are suited to the materials 
with which they deal. Techniques once initiated are capable of in- 
dependent development. As they are perfected, they not only 
transform old materials expeditiously and economically, but they 
are applied to crude materials previously not capable of use as 
means. The new formed-matter thus produced leads to further 
development of techniques and so on indefinitely, with no pos- 
sibility, from the theoretical side, of setting a limit. 

2. Any technique or set of procedural means must satisfy cer- 
tain conditions of order so that it possesses formal properties. The 
crudest technical procedure in reshaping crude material has, of 
necessity, a definite initiation, termination and an intermediation 
that connect the two limits. It has the formal properties of first, 
last and intermediates — the latter being so essential as to define 
even the word "means." The ordered transitive relation of first, 



LOGIC AND NATURAL SCIENCE 387 



last and middle operations is formal and capable of abstraction be- 
cause it constitutes a necessary interrelation of characters. Change 
any one of them and the others are necessarily also modified. 
Generalize the point here made and there emerges the conception 
of serial order as an order necessary to matter qua formed-matters 
from the point of view of all intelligent activity. 

3. Because of the first point mentioned (the conjugate corre- 
spondence of material and procedural means or techniques), the 
serial order of procedure determines formal relations in the mate- 
rials to which the techniques are applied. Even the crude primitive 
techniques employed to effect objective consequences brought 
about a crude differentiation between characteristic properties of 
materials. Certain materials were found to be "good for" the 
techniques by which clothing was produced; other materials for 
making utensils in which to store or to cook materials, etc. As 
techniques of smelting developed, characteristic differences in 
mineral materials were automatically, so to say, noted in such a 
way as to mark off different kinds of metals. The principle here 
exemplified is generalized in the statement that differential charac- 
teristics, describing different kinds, are instituted when and only 
when materials are adjudged as means in connection with opera- 
tions to accomplish specified objective consequences. An ac- 
complished end, say, clothing, is generic. But it comes about 
that different kinds of clothing are appropriate to different seasons, 
occasions, and social castes. Different materials are such as to be 
"good for" these differential ends: one kind for winter, another 
for summer; one for war and another for peace; one for priests, 
another for chiefs, and another for "common" people. Kinds 
are distinguished and related in strict correspondence with each 
other. 

Were we to recur to the considerations adduced in the chapter 
on the biological matrix of inquiry, we should note that the formal 
relations of serial order are prefigured in organic life. There are 
needs (in the sense of existential tensions); these needs can be 
satisfied only through institution of a changed objective state of 
affairs. Effectuation of this close, or consummatory state, de- 
mands an ordered series of operations so adapted to one another 
that they are co-adapted to arriving at the final close. If we com- 



388 THE LOGIC OF SCIENTIFIC METHOD 

pare these natural organic cases of means in ordered relation to a 
consequence one difference of importance appears. The "end" in 
the case of the relation of activities and material conditions is, in 
the case of the former, an end in the sense of a close or termina- 
tion. In the case of the latter, there is an additive character. The 
objective close in being foreseen and intended, becomes an end-m- 
vieiv and thereby serves to direct intelligent selection and arrange- 
ment of techniques and materials. But there is a common pattern 
of relationship. 

Upon the practical side, the considerations which have been 
brought forward are so familiar as to be commonplaces. They 
may seem, therefore, not worth noticing in the discussion of logi- 
cal theory. But they are pertinent because they bring out a num- 
ber of points that are fundamentally significant in logical theory. 
The main considerations may be recapitulated as follows: (1) The 
accruing of forms to matter in the case of inquiry is not a gratui- 
tous hypothesis. (2) Whenever materials become formed-ma- 
terials, there is involved a definite order, the serial. (3) This 
order, being formal, may be abstracted and be formulated in such 
a way that its implications are developed in discourse. (4) There 
is continuity of development from the orderly relations of organic 
life through the deliberately ordered relations of the cultural arts 
to these characteristic of controlled inquiry. 

It is important, in this connection, not to confuse the categories 
of potentiality and actuality. Crude materials must possess quali- 
ties such as permit and promote the performance of the specific 
operations which result in formed-matter as means to end. But 
(1) these qualities are but potentialities, and (2) they are dis- 
covered to be the potentialities which they are only by means of 
operations executed upon them with a view to their transformation 
into means-to-consequences. At the outset, these operations of 
transformation may be random and "accidental." In the progress 
of culture, they become so controlled that they are experimental 
in the scientific sense of that word. The first point is illustrated 
in the fact that with the emergence of animal life certain materials 
became foods. We may then say that these materials were foods 
all the time and even that they are intrinsically or "by nature" foods. 
Such a view confuses potentiality with actuality. Looking back, 



LOGIC AND NATURAL SCIENCE 389 



we can validly affirm that these materials were edible. But they 
are not foods in actuality until they are eaten and digested, i.e., un- 
til certain operations are performed that give crude materials those 
new properties which constitute them of the special kind foods. 
The second point is illustrated in the fact that the difference be- 
tween edible, non-edible, and poisonous properties was discovered 
only by processes of trying and testing. Even tribes regarded as 
primitive have found ways of instituting technical operations 
which transform stuffs that are poisonous in their crude state into 
means of nourishment. That qualities qua potentialities are ascer- 
tained by experimental operations is proved by the fact that with 
extension and refinement of physico-chemical operations the 
range of things that are edible has been indefinitely extended. 
Whether, for example, the attempt to produce milk "artificially" 
will succeed or not is wholly a matter of available techniques, not 
a theoretical matter save in the sense that some theory is necessary 
to guide practical effort. 

This relativity to operations of the qualities that constitute the 
characteristic traits which describe kinds, together with the rela- 
tivity of the discovery of the latter to execution of operations, is 
fatal, as we saw earlier, to the classic doctrine that inherent natures 
or essences define kinds. But it has another important bearing 
upon logical theory. The previous discussion has been limited 
to doctrines that make a sharp separation between form and mat- 
ter. But there still exist logical theories which assign direct onto- 
logical status to logical forms, although in a different way from 
that of Aristotelian logic. These theories rest upon a basis of fact. 
For they recognize that logical forms can apply to existential ma- 
terial only in a thoroughly ungrounded, external, arbitrary fashion 
unless material as existential has its own intrinsic capacity for tak- 
ing on these forms. But this valid insight is misinterpreted by 
means of the precise confusion of potentiality with actuality just 
mentioned. Existence in general must be such as to be capable of 
taking on logical form, and existences in particular must be capable 
of taking on differential logical forms. But the operations which 
constitute controlled inquiry are necessary in order to give actual- 
ity to these capacities or potentialities. 

The particular way in which in recent theory, logical forms 



390 THE LOGIC OF SCIENTIFIC METHOD 

are given direct existential status (instead of indirect status 
through their functions in inquiry) is a metaphysical interpreta- 
tion of invariants. The use of certain mathematically formulated 
constants in physical inquiry is an illustration, as far as it goes, of 
the meaning of an invariant in its logical sense. If we generalize 
what is involved, logical forms are invariants. For example, there 
is no ordered discourse apart from the implicatory relation as a 
constant, and there is no grounded inference apart from the in- 
variant formal relation of conjunction of traits to descriptive de- 
termination of kinds. But it does not follow from the fact that 
"invariants" are necessary for the conduct of inquiries that yield 
warranted knowledge that they are therefore necessary in and to 
the existence which knowledge is about. Under the guise of a 
valid principle, namely, that logical forms have existential refer- 
ence, there is slipped in quite another principle; namely, a particu- 
lar metaphysical conception about existence, and this special 
preconception is then used to settle the meaning of logical in- 
variants. Thereby logic is rendered heteronomous; or dependent 
upon a metaphysical principle not itself arrived at by logically de- 
termined methods. In scientific procedure, moreover, an invariant 
is such in relation to a specified set of operations, while the view 
criticized assumes that invariants are such absolutely. 

The external character of the metaphysical assumption is strik- 
ingly evident in that by definition it concerns existence, whereas 
inquiry into existence can only arrive at conclusions having a co- 
efficient of some order of probability. And it is obvious that con- 
ceptions of a probable invariant and an immutable structure are 
self-contradictory. Moreover, the conception is gratuitous. For 
the necessary operational presence of invariant forms in arriving 
(through inquiry) at warranted conclusions is completely ex- 
plicable on the ground of competently controlled conduct of in- 
quiry itself. Assumption of a one-to-one correspondence between 
the forms of authentic knowledge and the forms of existence does 
not arise from necessary conditions within the logic of inquiry. 
It proceeds from some outside epistemological and metaphysical 
source. r J 

The net conclusion of both the critical and constructive por- 
tions of the foregoing discussion is that the phrase "logic and 



LOGIC AND NATURAL SCIENCE 391 

scientific method" has no valid meaning when "and" is taken to 
mean an external relation between the two terms. For scientific 
method both constitutes and discloses the nature of logical forms. 
It constitutes them in the actual practice of inquiry 7 ; once brought 
into being, they are capable of abstraction: — of observation, analy- 
sis and formulation in and of themselves. In connection with this 
conclusion, it is pertinent to summarize briefly the outcome of 
some previous discussions. 

1. The history of actual scientific advance is marked by the 
adoption and invention of material devices and related techniques: 
- — of complex and refined forms of apparatus and definite related 
techniques of using apparatus. Even in the last half-century, 
astronomical science has been revolutionized by invention and 
use of such material instruments of inquiry as the spectroscope, 
bolometer, ultra-violet glass, chemical emulsions in photography, 
use of aluminum instead of mercury for coating mirrors, and the 
techniques which have made possible construction of lenses eighty 
inches in diameter and mirrors having a diameter of two hundred 
inches. 5 

2. The new data thus instituted do much more than provide 
facts for confirming and refining old conceptions. They institute 
a new order of problems whose solution requires a new frame of 
conceptual reference. In particular, it was by the use of new 
instruments and techniques that changes and relations of change 
were disclosed in what had previously been taken as fixed; a proc- 
ess that has gone on at an accelerated rate since the seventeenth 
century. This change in the nature of data was both the source 
and the product of the universal adoption of the experimental 
method and of the new order of conceptions demanded by its suc- 
cessful execution. 

3. Upon the conceptual side, this scientific revolution was ac- 
companied by a revolution in mathematical conceptions; again, 

5 Cf. ante, pp. 252-3. The following passage is worth citation as one of the 
comparatively few instances of recognition, from the side of theory, of the 
importance of this point: "The reason why we are on a higher imaginative 
level [in science] is not because we have finer imagination but because we 
have better instruments. In science, the most important thing that has happened 
in the last forty years, is the advance in instrumental design. . . . These instru- 
ments have put thought on a new level." A. N. Whitehead, Science and the 
Modern World, p. 166. 



392 THE LOGIC OF SCIENTIFIC METHOD 



partly as cause and partly as effect. As long as Euclidean geome- 
try was taken to be the exemplary model of mathematical method, 
the underlying categories of mathematics were such as to be ap- 
plicable only to structures fixed within certain limits. The logic 
of deduction from first, and immutable truths then remained 
supreme, wherever the necessity for general principles was ac- 
knowledged. Cartesian analytics, the calculus, and subsequent de- 
velopments were called for by the radically new emphasis placed 
in scientific inquiry upon correlations of change, while independ- 
ent development of mathematical conceptions disclosed in their 
application to existence new, more refined and extensive problems 
of correlated change. 

In the meantime, the development of a genuinely empirical 
theory of logic, one in accord with actual scientific practice, was 
seriously retarded and deflected by adherence to an order of ideas 
that had developed in the prescientific epoch. The incompatibil- 
ity of this conceptual framework with the actual procedures and 
conclusions of scientific inquiry strengthened, by reaction, the 
position of the non-empirical a priori school. Mill's logic, as 
representative of the earlier type of empiricism, is a noteworthy 
combination of genuine concern for scientific method as the sole 
source of valid logical theory with a misinterpretation of that 
method, which is due to an adherence to notions about sensations, 
particulars, and generalizations, that were formulated before the 
rise of modern scientific method. The outcome was his denial of 
the importance of conceptions; reduction of hypotheses to a 
secondary "auxiliary" position; the idea that mere particulars can 
"prove" a generalization, etc. 

This chapter, in both its critical and constructive phases, is, then, 
preparatory to detailed examination of the logic of scientific 
method, as that is exhibited in the mathematical and in the natural 
sciences. In a certain sense, the order of exposition of topics in 
this treatise is the reverse of the order in which their contents 
have actually developed. For, as just indicated, the special logical 
interpretations which have been advanced represent the conclu- 
sions of analysis of the logical conditions and implications of 
scientific method, while in the interpretations that form the pre- 
vious chapters they have been taken up, for the most part, on the 



LOGIC AND NATURAL SCIENCE 393 

ground of their logical status as such. The following chapters 
thus serve both as an explicit formulation of the ultimate founda- 
tions of the views previously expressed, and as a test of their 
validity. 

Because of the critical role of mathematics in physical science 
and because also of the peculiarly formal character of mathemati- 
cal subject-matter, the logical conditions of mathematical dis- 
course will be taken up first in order of the topics that are 
discussed. 



CHAPTER XX 
MATHEMATICAL DISCOURSE 



hrs/x iHE ability of any logical theory to account for the distin- 
guishing logical characteristics of mathematical conceptions 

)[ and relations is a stringent test of its claims. A theory such 
as the one presented in this treatise is especially bound to meet and 
pass this test. For it has the twofold task of doing justice to the 
formal character of the certification of mathematical propositions 
and of showing not merely the consistency of this formal charac- 
ter with the comprehensive pattern of inquiry, but also that 
mathematical subject-matter is an outcome of intrinsic develop- 
ments within that pattern. For reasons suggested in the closing 
sentence of the last chapter, the interpretation of the logical 
conditions of mathematical conceptions and relations must be 
such as to account for the form of discourse which is intrin- 
sically free from the necessity of existential reference while at the 
same time it provides the possibility of indefinitely extensive exis- 
tential reference— such as is exemplified in mathematical physics. 

L Transformation as a Fundamental Category. The end of in- 
quiry (in the sense in which "end" means both end-in-view, or 
controlling intent, and terminating close) is institution of a unified 
resolved situation. This end is accomplished by institution of 
subject-matters which are respectively material means and pro- 
cedural means— factual data and conceptual meanings. These in- 
strumental subject-matters are instituted by operations in which 
the existential material of a given problematic situation is experi- 
mentally modified in a given direction. Conceptual subject-matters, 
consisting of possibilities of solution, are at the same time so con- 
structed as to direct the operations of experimental selection and 
ordering by which transformation of existential material toward 
the end of a resolved situation is effected. The conceptions that 



MATHEMATICAL DISCOURSE 395 



represent possibilities of solutions must, moreover, if inquiry is 
controlled, be propositionally formulated- and these propositions 
must be developed in ordered series so as to yield a final general 
proposition capable of directing in operations definitely applicable 
to the material of the special problem in hand. Otherwise, there 
is an inference so premature as to yield an ungrounded proposition. 

In short, ordered discourse is itself a series of transformations 
conducted according to rules of rigorous (or necessary) and fruit- 
ful substitution of meanings. Such transformation is possible only 
as a system of interrelated abstract characters is instituted. Com- 
mon sense conceptions, for example, do not satisfy the conditions 
of systematic interrelation. Hence the change of content they un- 
dergo in science as they are modified to satisfy this condition. 
Transformation of conceptual contents, according to rules of 
method that satisfy determinate logical conditions, is thus involved 
both in conduct of discourse and in the formation of the concep- 
tions that enter into it even when discourse is intended to have 
final existential application. 

The logical principle involved may be restated in the following 
ways: (1) The subject-matter or content of discourse consists of 
possibilities. Hence the contents are non-existential even when 
instituted and ordered with reference to existential application. 
(2) As possibilities, they require formulation in symbols. Sym- 
bolization is not a convenience found to be practically indispensa- 
ble in discourse, nor yet a mere external garb for ideas already 
complete in themselves. It is of the very essence of discourse as 
concerned with possibilities. In their functional capacity, how- 
ever, symbols have the same logical status as existential data. For 
this reason they are themselves subject to transformations. His- 
torically, the operations by which symbol-meanings are trans- 
formed were first borrowed from and closely allied to physical 
operations — as is indicated in the words still used to designate 
rational operations; in gross, in such words as deliberation, ponder- 
ing, reflection, and more specifically in counting and calcidation. 
As meanings were modified to satisfy the conditions imposed by 
membership in an interrelated system, operations were also modi- 
fied to meet the requirements of the new conceptual material. 
They became as abstract as the materials to which they are ap- 



396 THE LOGIC OF SCIENTIFIC METHOD 



plied and hence of a character expressed, and capable only of ex- 
pression, in a new order of symbols. 

In the chapters preceding the present one, we have been con- 
cerned with the relation of meanings and propositions in discourse 
where discourse is conducted in reference to some final existential 
applicability. In discourse of this type application is suspended 
or held in abeyance but relationship to application is not eliminated 
in respect to the content of the conceptions. When, however, 
discourse is conducted exclusively with reference to satisfaction 
of its own logical conditions, or, as we say, for its own sake, the 
subject-matter is not only non-existential in immediate reference 
but is itself formed on the ground of freedom from existential 
reference of even the most indirect, delayed and ulterior kind. 
It is then mathematical. The subject-matter is completely abstract 
and formal because of its complete freedom from the conditions 
imposed upon conceptual material which is framed with refer- 
ence to final existential application. Complete freedom and com- 
plete abstractness are here synonymous terms. 

Change in the context of inquiry effects a change in its intent 
and contents. Physical conceptions differ from those of common 
sense. For their context is not that of use-enjoyment but is that 
of institution of conditions of systematic extensive inference. A 
further new context is provided when all reference to existential 
applicability is eliminated. The result is not simply a higher degree 
of abstractness, but a new order of abstractions, one that is insti- 
tuted and controlled only by the category of abstract relationship. 
The necessity of transformation of meanings in discourse in order 
to determine warranted existential propositions provides, neverthe- 
less, the connecting link of mathematics with the general pattern of 
inquiry. 

The effect of change of context upon the intent and contents 
of operations was exemplified in some of the illustrations that were 
adduced in the previous chapter. Categories of selection and 
order, having an implicit esthetic quality, are involved in the writ- 
ing of history. These categories when liberated from their origi- 
nal context gave rise to the historical novel. Carried further, they 
give rise to the "pure" novel with its distinctive contents. In 
similar fashion, music did not create in either nature or in speech 



MATHEMATICAL DISCOURSE 397 

sounds and their ordered arrangement. Music, however, de- 
veloped the potentialities of sounds and their cadenced arrange- 
ment in activities having their own distinctive subject-matter. An 
analogy with development of mathematics is not forced. Numeri- 
cal determinations first arose as means of economic and effective 
adjustment of material means to material consequences in qualita- 
tive situations marked by deficiency and excess. 1 But not only was 
there nothing in the operations that were involved to obstruct 
development on their own account, but they invited such de- 
velopment. 

The complete execution of the abstraction involved was a slow 
historical process. Doubtless numbers were first closely con- 
nected with things. For example, 2, meant two fingers or two 
sheep, and, as the word geometry still suggests, geometrical con- 
ceptions were associated with physical operations of measuring 
physical areas. Greek mathematicians and philosophers effected a 
partial liberation from existential reference. But abstraction was 
not complete. Conceptions of arithmetic and geometry were 
freed from reference to particular things but not from all ontologi- 
cal reference. For they were supposed to refer to the metes and 
bounds existing in nature itself by which nature was an intelligible 
structure and by which limits were set to change. Since geometry 
was the science of these existential cosmic "measures," number 
was geometrically conceived. The story of liberation of mathe- 
matical subject-matter from any kind of ontological reference is 
one with the story of its logical development through a series of 
crises, such as were presented by irrationals, negatives, imaginaries, 
etc. 

II. The Two Types of Universal Propositions. The foregoing 
introductory remarks are intended to indicate that the category 
of transformation extends through the whole pattern of inquiry 
from (1) existential transformations that are required in order 
to warrant final judgment, to (2) meanings in discourse, and to 
(3) the formal relations of completely abstract subject-matters, in 
which transformation as abstract possibility takes the form of 
trmsiormability in the abstract. As a consequence of the last 
named development, two logical types of universal propositions 
1 See, ante, pp. 209-10. 



398 THE LOGIC OF SCIENTIFIC METHOD 

must be distinguished. In the course of previous discussions it has 
been held that a physical law, such as is expressed as a relation of 
abstract characters, is a universal hypothetical proposition. For 
example, the law of gravitation is a formulation of the interrelation 
of the abstract characters mass, distance and "attraction." But 
while the contents of the proposition are abstractions, nevertheless, 
since the proposition is framed with reference to the possibility of 
ultimate existential application, the contents are affected by that 
intent. Such hypothetical universals do not exhaust the possible 
existential affairs to which they may be applied, and as a conse- 
quence may have to be abandoned in favor of other hypothetical 
universals which are more adequate or appropriate to the subject 
at hand. This is illustrated by the change from the Newtonian 
law of gravitation to the Einsteinian formulation. Although both 
are hypothetical universals in this sense, each is an empirically 
significant contrary of the other. In such propositions (including 
all those of mathematical physics) the strictly mathematical phase 
resides in the necessary relation with propositions sustain one to 
another, not in their contents. 

But in a mathematical proposition, such as 2 -f 2 = 4, the inter- 
pretation to be put upon the contents is irrelevant to any material 
considerations whatever. The final applicability of a physical 
law, even when stated as a universal hypothesis, demands that some 
preferred and therefore some limiting interpretation be placed 
upon the terms or contents that are related. The contents of a 
mathematical proposition are freed from the necessity of any 
privileged interpretation. Take the physical law of the parallelo- 
gram of forces, as that provides the basis of calculations ultimately 
applicable in existential determination. The status of "forces'' in 
that law affects the meaning of "parallelogram"; it limits the other- 
wise mathematical conception to subject-matters having properties 
of direction and velocity. That is, it requires what was called a 
preferred or privileged interpretation, which is restrictive. The 
contents of a mathematical proposition, qua mathematical, are 
free from the conditions that require any limited interpretation. 
They have no meaning or interpretation save that which is for- 
mally imposed by the need of satisfying the condition of trans- 
formability within the system, with no extra-systemic reference 



MATHEMATICAL DISCOURSE 399 

whatever. In the sense which "meaning" bears in any conception 
having even indirect existential reference, the terms have no mean- 
ing — a fact which accounts, probably, for the view that mathe- 
matical subject-matter is simply a string of arbitrary marks. But 
in the wider logical sense, they have a meaning constituted ex- 
clusively and wholly by their relations to one another as deter- 
mined by satisfaction of the condition of transformability. This 
type of universal hypothetical proposition is therefore logically 
certifiable by formal relations, because formal relations determine 
also the terms or contents, the "material," as they cannot do in 
any universal proposition having ultimate existential application. 
The type of relation which subsists between propositions in mathe- 
matical physics becomes here the determinant of the contents. 

To summarize, transformation of meanings and their relations 
is necessary in the discourse that is conducted to take ultimate effect 
in existential transformations. The involved operations of trans- 
formation are capable of being themselves abstracted; when ab- 
stracted and symbolized, they provide a new order of material in 
which transformation becomes transform^iitfy in the abstract. 
Control of transformations that take place in this new dimension 
of subject-matter is exercised solely by reference to satisfaction of 
conditions of transformability in the abstract. 

III. The Category of Possibility. This theory of mathematical 
subject-matter continues the emphasis that has throughout been 
placed upon operational determination of the subject-matters of 
inquiry. The logical import of this operational determination in 
this particular context may be brought out by contrasting the 
operational interpretation of possibility (with respect to trans- 
formability) with another theoretical interpretation of its nature. 
This other theory differs in holding to an ontological as over 
against an operational interpretation of possibility, for it relates 
mathematical (and logical) forms to a Realm of Possibility con- 
ceived to have ontological status. The realm of possibility is in- 
definitely more extensive than the realm of actuality, and, since 
what is actual must be first possible, it provides the ultimate logi- 
cally limiting ground for whatever is actual. The applicability 
of logic and mathematics to existence is accordingly explained to 
be a special instance of the general relation of the realm of possible 



400 THE LOGIC OF SCIENTIFIC METHOD 



Being to that of actual Being. This theory is here brought under 
discussion because it affords, by way of contrast, opportunity to 
bring out more explicitly the implications of the functional- 
operational interpretation of possibility. For the question does 
not concern the basic importance of that category but its inter- 
pretation. 

It is not a simple matter to find illustrative material such as will 
take the discussion out of the domain of direct clash of philo- 
sophical theories into the domain of logic proper. A point of de- 
parture may be found, however, in the question of the relation 
a map of a country bears to the country of which it is a map. 
The illustration is but a point of departure, for clearly it cannot 
be supposed to provide a direct analogy. For the country mapped 
is an example of the existential Realm of Being, and the map refers 
to the country of which it is the map as to an existence. The force 
of the illustration, as analogical, resides somewhere else; namely, 
in the isomorphism of the relations of the map and the country, in- 
dependently of the existential nature of the relations of the latter. 

That the isomorphism in question is one of relations is evident 
in the fact that it does not exist between a point marked on the 
map and an element of the country mapped, town, river, moun- 
tain, but between the relations sustained by the former and the 
relations sustained by the latter. Relations of up-down in the 
map are isomorphic with relations of north-south in the country, 
and those of right-left with those of east-west of the country. 
Similarly, relations of distance and direction of the map are iso- 
morphic with those of the country, not literal copies of actual 
existences. The illustration will be used to indicate that the iso- 
morphic relation which subsists between the relations of the map 
and those of the country, or between patterns of relation, should 
be interpreted in a functional and operational sense. 2 

A beginning may be made by noting the ambiguity of the word 
relation. It stands not only for existential connections, for logical 
relations between the terms of a proposition, and for reference or 
applicability of the proposition to existence — but also for relation- 
ship. 3 The first set of ambiguities does not concern the argument 

2 In other words, the issue concerns the meaning of isomorphic patterns, not 
their existence or importance. 

3 For the former, see ante, pp. 54-5. For the latter, ante, pp. 330-2. 



MATHEMATICAL DISCOURSE 401 

regarding isomorphism in the case of mathematics. For while on 
general logical principles it is necessary to distinguish the existen- 
tial connections of the country from the logical relations of the 
map as a proposition, and both of these from the reference which 
the map has to the country, the distinctions are not relevant to the 
present issue, since the order of Being with which mathematical 
relations are said to be isomorphic is non-existential. Nevertheless, 
two points about the "relation" (reference) of a map to the 
country mapped will be made because of their bearing upon the 
nature of isomorphism. 

1. The relations of the map are similar (in the technical sense 
of that word) to those of the country because both are instituted 
by one and the same set of operations. As far, then, as this case 
of similarity of relations is an illustration of isomorphism, it throws 
no light on the ontological isomorphism said to subsist in the case 
of mathematics. For that doctrine is at the opposite pole. It does 
not hold that operations that determine the relations of mathemati- 
cal subject-matter also determine those of the "Realm of Possi- 
bilities." The position here taken does hold, however, that the 
operations of transformability which determine mathematical sub- 
ject-matter are, or constitute, the Realm of Possibilities in the only 
meaning logically assignable to that phrase. 

The statement that the relations of the map are similar to those 
of the country mapped because both are instituted by one and the 
same set of operations is readily seen by noting the fact that both 
are products of execution of certain operations that may be summed 
up in the word surveying. The elements of the country are cer- 
tainly existentially connected with one another. But as far as 
knowledge is concerned, as far as any propositions about these 
connections can be made, they are wholly indeterminate until the 
country is surveyed. When, and as far as, the country is surveyed, 
a map is brought into being. Then, of course, there is a common 
pattern of relations in the map and in the country as mapped. Any 
errors that result in the map from inadequacy in the operations of 
surveying will also be found in propositions about the relations of 
the country. The doctrine of structural (in the sense of non- 
operational) similarity of the relations of the map and those of the 
country is the product of taking maps that have in fact been per- 



402 THE LOGIC OF SCIENTIFIC METHOD 

fected through performance of regulated operations of surveying 
in isolation from the operations by which the map was constructed. 
It illustrates the fallacy that always occurs when propositions are 
interpreted without reference to the means by which they are 
grounded. 

2. Given the map as a pattern of relations, the "relation" of the 
the pattern to that of the country mapped is functional. It is con- 
stituted through the intermediation of the further operations it 
directs — whose consequences, moreover, provide the means by 
which the validity of the map is tested. The map is instrumental 
to such operations as traveling, laying out routes for journeys, 
following movements of goods and persons. If this consideration 
is employed with respect to mathematical subject-matter, it must, 
of course, be noted that the further operations which the two 
respective subject-matters direct are of different forms. In the 
case of mathematics the operations and consequences are not ex- 
istential as they are in the relation of the map to traveling, etc., 
and their consequences. But as far as development of mathemati- 
cal subject-matter as such is concerned the analogy concerning the 
functional use of operations is precise. The reference of mathe- 
matical subject-matter that is given at any time is not ontological 
to a Realm of Possibilities, but to further operations of transforma- 
tion. 

As far as the map is usable as an illustration of mathematics, the 
isomorphic relation is definitely exemplified in the relation to one 
another of maps that are drawn upon different projection systems. 
The pattern of relations of a map drawn upon the Mercator pro- 
jection is isomorphic with that of maps drawn upon conic, cylin- 
drical and stereographic projections, while theoretically still other 
isomorphic projection-systems are possible. There is a morpho- 
logical enlargement of polar regions in the Mercator style of map; 
in the cylindrical, their shape is distorted, while areas are correct; 
in the stereographic, areas are correctly patterned but the scale 
is not constant throughout all parts of the map, etc. When the 
directive function of the map is left out of consideration it must 
be said that no map is "true," not only because of the special "dis- 
tortions" mentioned but because in any case a map represents a 
spherical upon a plane surface. On the functional interpretation, 



MATHEMATICAL DISCOURSE 403 

any map in any system is "true" (that is, valid) if its operational 
use produces the consequences that are intended to be served by 
the map. 4 Considering only the relationship of their patterns, 
there is isomorphism because the relations characteristic of one are 
transformable inclusively and exclusively into the relations of every 
other. 

What is involved in the last paragraph, as far as illustration of 
mathematical subject-matter is concerned, introduces the topic of 
the ambiguity in the term relations and relational with respect to 
the distinction of form between relatives and relationships. Terms 
are related to each other in the sense of being relative whenever 
they involve, in addition to the specific relation designated, singu- 
lars or kinds which have traits and relations over and above the 
relation which is specified: when, that is, the relation in question 
does not exhaust the significance of the related terms. Father and 
son are relative terms whether applied to two given singulars or 
to two kinds. But the singulars who are fathers and sons have 
many other traits and relations. Indeed, they are related to each 
other only because they have other properties. But paternity - 
sonship is a term in which the "relation" exhausts the meaning of 
the terms. The difference is that expressed linguistically re- 
spectively by "concrete" and "abstract" nouns. Furthermore, 
there is no necessary relation such that the man who is related as 
a father is also related as a brother. The question of whether he 
is a brother is a question of fact to be determined by observation. 
But there is possible a system of relationships , such that "within the 
system paternity and brotherhood are necessarily related, while also 
both are interrelated, by the very structure of the system, with 
uncleship, cousinship, and so on, as in an abstract genealogical 
table which exhaustively includes every relationship in a system 
of possibilities of kinship. In the ordinary Mercator map, if the 
polar regions were taken to be relative (in the sense defined) to 
equatorial regions, there would be misrepresentation. But given 
the coordinates which define the projective system, they have a 
necessary relationship within the system. When mathematical 

4 Interpretation of "truth" as correspondence in terms of literal reproduction 
would demand that a "true representation" be another globe just like the earth 
itself. Such a reproduction would be useless for the purpose representation ful- 
fills. It would, in fact, only duplicate the problems of the original. 



404 THE LOGIC OF SCIENTIFIC METHOD 

subject-matter is said, then, to consist of relations of relations, the 
statement is ambiguous. In the case of singulars and of kinds, 
"relations of relations" always involve reference, implicit or ex- 
plicit, to materials (of singulars and kinds) whose existence or 
non-existence can be determined only through observation. With- 
out such reference to elements as terms of the relations that are 
related, it (relations of relations) is an absurd conception. But 
relationships by their very nature are interrelated in a system—, 
the nature of the system being determined in mathematics by a 
set of postulates. 

A system of relationships defined as being of a given order — as in 
the case of a map projection or an abstract genealogical table— 
constitutes, therefore, the ground of operations of transformation 
within that system. Indeed, this statement is too weak in that it 
fails to note that the system of interrelated meanings is so defined 
as to make possible a set of operations of transformations in which, 
on formal grounds — those determined by the postulates of the 
system — any given transformation is logically necessary. In a 
weakened sense, the relationships of maps drawn on different pro- 
jective systems and the relationships of the abstract genealogical 
system are mathematical in quality. But mathematics proper is 
constituted by abstraction of the operation of possible transforma- 
tion (transformability) so that its subject-matter is universalized 
in a way which is not found in the instances cited. While it is 
not claimed that this operational-functional interpretation of iso- 
morphic patterns of relationships disproves the interpretation of 
mathematics that refers it to an ontological ground, it is claimed 
that it renders that interpretation unnecessary for logical theory, 
leaving it in the position of any metaphysical theory that must be 
argued for or against on metaphysical grounds. 

IV. The Fostulational Method. The previous discussion is 
meant to indicate that and how the general pattern of inquiry is 
reflected in mathematics — the function of abstraction which is in- 
volved in all existential inquiry being itself abstracted and uni- 
versalized. Further discussion will attempt to show in more specific 
terms how the pattern is exhibited in the postulational method of 
mathematics. 

1. The initiation of every inquiry springs from the presence of 



MATHEMATICAL DISCOURSE 405 

some given problematic subject-matter. In its early history, 
problems of strictly existential subject-matter provided the occa- 
sion for mathematical conceptions and processes as means of re- 
solving them. As mathematics developed, the problems were set 
by mathematical material as that itself stood at the given time. 
There is no contradiction between the conceptual, non-existential 
nature of mathematical contents and the existential status of mathe- 
matical subject-matter at any given time and place. For the latter 
is an historical product and an historical fact. The subject-matter 
as it is at a given time is the relatively "given." Its existing state 
occasions, when it is investigated, problems whose solution leads 
to a reconstruction. Were there no inconsistencies or gaps in 
the constituents of the "given" subject-matter, mathematics would 
not be a going concern but something finished, ended. 

2. As was intimated in an earlier context, material means and 
procedural means operate conjugately with each other. Now 
there are material means, having -functionally the status of data, in 
mathematics in spite of their non-existential character. They con- 
stitute the "elements" or "entities" to which rules of operation 
apply, while the rules have the function of procedural means. 
For example, in the equation 2 + 3=5, 2 and 3 are elements 
operated upon, while + and = are operations performed. There 
is no inconsistency in the identity between the logical junction 
of existential data and mathematical elements or entities and the 
strictly non-existential character of the latter. On the contrary, 
the condition of transformability which mathematical contents 
must satisfy demands that there be "data" which are determined 
exclusively and exhaustively by reference to the operations and 
rules of operations executed or to be executed with and upon 
them. 

In any existential inquiry also, material data are selected and 
ordered with reference to operations to be performed, the latter 
being possibilities formulated in hypothetical propositions. But 
the qualities which are selected and ordered as evidential traits are 
selected from out of a total existential situation and are themselves 
existential. Hence they are capable of only a specific and limiting 
interpretation, since anything existent is spatially and temporally 
circumstantial and local. Consequently, as we have seen, the 



406 THE LOGIC OF SCIENTIFIC METHOD 



contents of physical non-existential generalizations are determined 
with reference to final existential applicability; the fact that they 
are formulated so as to be as comprehensive as possible (as applica- 
ble to the widest possible range of existences) does not eliminate 
their final determination in terms of existential applicability. The 
generalizations instituted do eliminate reference to all existential 
qualities and circumstances that might restrict the applicability of 
the generalization; but such elimination is compensated for, and, 
indeed, is constituted, by selection of more generic extensive ex- 
istential traits. 5 The conceptual nature of the material data of 
mathematics means that they are determined exclusively and 
wholly in reference to the possibility of operations of transforma- 
tion, the latter constituting procedural means. This property is 
all one with that freedom from specific and hence limiting in- 
terpretation that has already been mentioned. 

Discussion is thus brought to explicit consideration of the postu- 
lational method of mathematics. Any scientific system, when 
logically analyzed and ordered, is found to involve certain propo- 
sitions that are, for that system, primitive. These primitive propo- 
sitions are postulates in that they state demands to be satisfied by 
the derived propositions of the system. In the systems of natural 
science, the demands to be satisfied involve (1) elements deter- 
mined by controlled or experimental observation and (2) opera- 
tions which are capable of existential execution. The primitive 
propositions which are the postulates of a mathematical system 
are, as has been shown, free from both of these conditions. For 
their contents with respect to both elements and methods of 
operation are determined exclusively with reference to trans- 
formability. 

The postulates of a mathematical system, in other words, state 
elements and ways of operating with them in strict conjugate 
relation each to the other. Take, for example, such a postulate 
as the following: "If a and b are elements of the field K, then ab 
{a X b) are elements of K." The postulated elements are a, b. 
The postulated operations are represented by "and" and by "X" 

5 The concrete bearing of this determination is considered later with reference 
to M, T and L, as standard conceptual means of selecting and ordering data. 
Ch. XXIII, pp. 481-3. 



MATHEMATICAL DISCOURSE 407 

or ab. The primitive proposition does not first postulate certain 
elements, and thereby means of another primitive proposition pos- 
tulate a certain operation in two separate postulates. The elements 
and the operations are laid down in a single postulate in logical de- 
pendence each upon the other, a is defined to be such that if the 
operation designated by and is applicable, then the operation sym- 
bolized by X is necessarily applicable. The elements are insti- 
tuted in relation to the operations by which they are related and 
the operations and their rules are determined in reference to the 
elements. The operations which are introduced by the postulates 
are specified in no other way than by the combinations into which 
they are permitted to enter by the postulates. For example, the 
operation denoted by "X" is any operation whatsoever, provided 
only that it satisfies the conditions of commutativity, associatativ- 
ity, and distributivity with respect to the operation denoted 

by"+." 

For this reason description and definition, which are of different 
logical forms in the case of existential material, coincide with re- 
spect to the elements or material data of mathematical subject- 
matter, as do also inference and implication. The elements are 
what they are defined to be; constituted by definition and nothing 
but definition. The methods of operation, which are postulated 
in conjugate relation with the elements are, on the other hand, 
resolutions rather than definitions. Neither the definitions nor the 
resolutions can be identified with axioms in the traditional sense of 
self-evident truths. The resolution concerns methods of procedure 
to be strictly adhered to, and the definition posits elements to be 
operated with and upon by these specified methods of combina- 
tion, yielding transformations stated in the theorems that follow. 
There is no other control of their meaning, which means that the 
control is strictly formal. They are not controlled, as in the early 
logical philosophy of mathematics, by extra-systemic reference to 
some "essence." 

Every scientific system is constituted by a set of postulates, 
which in logical ideal are independent of one another, or that do 
not overlap as to operations to be performed. For a combination 
of operations is the only way in which development in discourse 
can take place. The postulate mentioned above is a way of setting 



408 THE LOGIC OF SCIENTIFIC METHOD 



forth the principle that any element subject to the condition of 
logical summation is also subject to that of alternation. Another 
postulate, namely, that if a is an element of the field K, then a is 
also an element, states that any posited element that can be affirmed 
is also subject to the operation of negation, thereby fulfilling the 
logical condition of the conjugate relation of the functions of 
affirmation and negation. Since the constituent primitive proposi- 
tions of a set of postulates prescribe a complex of operations by 
means of which the results of one operation may be combined 
with results of other operations, postulates in one system may 
appear as theorems in another system and vice-versa. For the sole 
ultimate logical condition to be satisfied is that the postulates define 
elements and prescribe ways of dealing with them in combinations 
of operations such that theorems follow which satisfy all the con- 
ditions of formal conjunction-disjunction. 

Any single operation taken by itself is indefinitely recurrent or 
non-terminating. This is true of even a physical operation like 
walking or chopping wood. Single operations do not provide 
the conditions of their own termination. They are brought to a 
close only when cut across or intercepted by an operation of an 
opposite direction. In other words, a combination of operations 
and of their results may be called interceptive, a typical, although 
limiting, instance being the relation of affirmation and negation 
already mentioned. At this point, however, we are concerned 
with the indefinitely iterative nature of any operation in and of 
itself. For this character gives the ground for what has been 
called "mathematical induction." Its nature is illustrated by the 
following: The sum of the first n add integers is n 2 . For this prop- 
erty holds for the case when n is equal to 1 ; and we can show that 
if this property holds for n = k it also holds for n = k + 1. 
Consequently, it holds for every value of n, since every value of n 
can be obtained from 1 by the recurrent operation of adding 1. 
Because of inability to derive this principle from other proposi- 
tions, it has been held, as by Poincare, to be an "intuition of the 
mind." In fact, it is a formulation of the inherently recurring 
nature of any operation until it is intercepted by combination 
with another operation or is delimited by a field like the transfinite 
numbers in which operations do not have the inductive property. 



MATHEMATICAL DISCOURSE 409 

It is neither a postulate nor an intuition, but a partial description 
of the nature of the operations that are postulated in a given 
system. 

Combination of operations that are integrated with another and 
also intercepted by a limiting operation, yield in the case of the 
system of numbers, numbers which are sums (or products, differ- 
ences), and w T hich, in virtue of the integration of operations, are 
also integers. 6 Thus 748 which is a sum, or a difference or a 
product with respect to the operations by which it is instituted is 
also a number which may be treated as itself an integer in further 
operations. Were it not for the principle illustrated in this com- 
monplace instance the indefinite because abstract transformability 
characteristic of mathematical subject-matter would not exist. 

— 1 X 1 

1, i, 1 X 1, V 1 , 1\ , — - — ' are products of different operations 

and with respect to the operations by which they are instituted 
are distinct, as is perhaps more obvious in the case of 1 as the limit- 
ing sum of the infinite series i, i, i, . - . But further operations 
may operate with any one of these results either with or without 
reference to the operations by which it was instituted according 
to the exigencies of the problem in hand, if only the postulates of 
the system are not violated. If this were not so, the conditions of 
abstract transformability could not be satisfied, for barriers would 
be set up such as once were supposed to exist in the case of "ir- 
rationals." 

This principle is the basis of the operations of contraction (sim- 
plification) and expansion (composition) which play such a role 
in mathematics. The operative combination of a variety of 
operations is symbolized by a vinculum or bracket. The result 
of the combination of operations may be represented by a simple 
expression which can then be operated with and upon without 
reference to the complex of operations symbolized by the contents 
within a parenthesis. This simplification is another exemplification 
of the principle that transformability is the ultimate logical cate- 
gory, and that all mathematical operations must be such as maintain 

6 1 owe to Dr. Joseph Ratner the point that a "transfinite" number is such 
because the operations by which it is instituted are non-integratable. By defini- 
tion it is not an integer. This does not mean that operations of transforma- 
tion cannot be executed with and upon transfinites. 



410 THE LOGIC OF SCIENTIFIC METHOD 

or promote transformations with respect to the postulates of the 
system. 7 

Within a given system, accordingly, equivalence is always an 
end-in-view or object to be attained. In accordance with the 
position previously set forth, as an end-in-view it functions also 
as a means in discriminative ordering of the conditions of its at- 
tainment. In mathematics, equivalence takes the form of an 
equation. In existential inquiry, equivalence and substitutability 
are effected with reference to final existential applicability and are 
hence limited by the condition thus imposed. In mathematics, 
since equivalence (equations) is the end-in-view to be attained 
within a given system and an operative rule in discriminative or- 
dering of elements, differences in the operations by means of which 
contents in the system are determined are irrelevant with respect 
to further operations (as they are not in discourse intended to 
yield universal propositions that are existentially applicable), pro- 
vided their results so satisfy the condition of a finally attained 
equivalence or equation that they are capable of being taken, either 
in simplified or expanded form, as the material of further opera- 
tions of transformation. 

Equivalence is the end-in-view within the system determined by 
a given set of postulates. When different sets of postulates de- 
termine different systems, the conditions for satisfaction of 
equivalence as between them are not found. But universal trans- 
formability demands that the theorems of any one system be trans- 
latable into the theorems of the other systems. This reciprocal 
translatability is effected through institution of isomorphism; that 
is, isomorphism (like that of maps of different projection systems) 
is to transf ormability between systems what equivalence is to trans- 
formation within a system. The institution of inter-systemic 

7 The reader who is familiar with current logical literature may have noticed 
that the canons discussed in Chap. XVII were limited to identity, contradiction 
and excluded middle, while it is now usual to include along with them reitera- 
tion, association, distribution, simplification, absorption, composition, etc. The 
omission of the latter was deliberate. For the first three canons represent condi- 
tions to be satisfied in final judgment while the others mentioned belong to the 
calculus of propositions, stating rules of abstract transformability of proposi- 
tions. Hence, their applicability is relative to the postulates of a given system. 
Commutation with respect to combination of vectors has, for example, a dis- 
tinctive mathematical content. 



MATHEMATICAL DISCOURSE 411 



transf ormability requires, however, the institution of a new system 
as intermediary. It is as if translation of Greek, Latin, German, 
French, English, etc., into one another required the institution of 
a new language or set of symbols. For example, the distinctive 
results of algebra and geometry were rendered isomorphic by in- 
stitution of analytic geometry. It is characteristic of the abstract 
universality^ of the transf ormability category in defining mathe- 
matical subject-matter that the institution of any given mathe- 
matical system sooner or later sets the problem of instituting a 
further branch of mathematics by means of which its characteristic 
theorems are translatable into those of other systems— a considera- 
tion that helps to explain the indefinite fertility of mathematical 
developments. 

Interceptive combination of operations determines the important 
mathematical category of periodicity or grouping. The orioinal 
historic source of periodic arrangement was doubtless existential. 
It has been surmised, for example, that the first name for 2 was 
derived from some natural grouping, such as the wings of a bird, 
and the name for 3 from, say, the symmetrical arrangement of 
leaves in trefoil. However this may be, there is no doubt that 
the periodic grouping constituting our decimal system was derived 
by suggestion from the existential fact of ten fingers and/or ten 
toes. While the decimal system is conventional in historic origin, 
some form of periodic grouping (independent of course, of ex- 
istential considerations) is necessary, not conventional. Unless 
combinations took the form of recurrence of groupings of opera- 
tions (or were it limited to recurrence of operations in their 
severalty) there would be no integration of operations already 
performed. While grouping is especially conspicuous in the re- 
current position of 10 in our decimal system, the principle is ex- 
emplified in any number, say 2. Otherwise there would be simply 
a non-numerical succession as in the successive ticks of a clock 
when they are not integrated in relation to one another. In an 
infinite series, periodicity is dependent upon the partially non- 
integratable character of the operations by which it is instituted, 
and conversely any number as an integer is an integration of opera- 
tions that express and determine some periodicity of arrangement. 
The concepts of line, plane, solid, with their subcategories, are 



412 THE LOGIC OF SCIENTIFIC METHOD 



examples of integrated groupings. If prima facie the same state- 
ment does not seem to hold of the conception of a point, the 
identity appears when the complete relativity of its conception to 
that of lines, planes and solids is noted. Indeed, it may be said 
that the mathematical point, like the mathematical instant, makes 
explicit the conception of abstract intervalness involved in abstract 
periodicity. 

The conclusions reached may be applied to the interpretation of 
zero and infinity. The conjugate relation of affirmation and nega- 
tion (identification-demarcation, inclusion-exclusion) in determi- 
nation of any completely warranted conclusion has been repeatedly 
pointed out in the context of different logical topics. This condi- 
tion cannot be completely satisfied in existential inquiry because 
the existential conditions of any inferred proposition do not consti- 
tute a closed system. Hence, the probable, as distinct from neces- 
sary, nature of such propositions. Mathematical subject-matter 
is so formally instituted that the condition is fulfilled. The posi- 
tive and negative are completely conjugate with each other, so that 
it might be said that a primary standing rule is that no operation 
should do anything that another operation cannot undo. is not, 
then, a symbol for sheer nullification of operations, nor yet, as in 
the case of the null class in existential propositions, a symbol of 
a kind that is empty at a given time. It is a symbol for the com- 
plete and necessary balance of operations of identification-demarca- 
tion, inclusion-exclusion. This conjugation finds a simple expres- 
sion in such an equation as a — b — 0. 

The positive logical function performed by is that without it 
operations that effect complete transformability are lacking. In 
the series of integers, for example, negative numbers have no legiti- 
mate warrant without 0, which, as a number, introduces the func- 
tion of direction. A better example is found in analytics in which 
is the point of origin of all vectors within the system. With 
respect to it, as the center of a system of co-ordinates, free gen- 
eralized possibility of operations in all directions is instituted, with 
results that are so determined that they are related contents within 
a defined system of transformations. On the other side, as the 
symbol of the center of a coordinately determined system, is a 



MATHEMATICAL DISCOURSE 4H 

symbol for the completely integrated relation that affirmative and 
negative functions sustain to each other. 

The infinite in the sense of the non-terminating is a symbol for 
the intrinsically recurrent nature of any operation whatever taken 
in its severalty. The infinitude of number or the infinitude of a 
line (as distinct from lines as segments characteristic of Euclidean 
o-eometry) is not then an infinite number or an infinite line. In 
modern mathematical philosophy, another and more generalized 
meaning is given to the conception of the infinite. The meaning 
is that of correspondence, and in particular that of the corre- 
spondence of a proper part to the whole of which it is a part 
Since the category of correspondence is involved in the possibility 
of transformation (in the case both of equivalence within a system 
and isomorphism between systems), a logical problem arises as to 
whether correspondence in this definition of the infinite is to be 
interpreted operationally or in some other way. In its operational 
sense, the doctrine that infinity means that sets are "equal" to 
proper parts of themselves sets forth the possibility of operational 
institution of correspondences of an isomorphic nature. It might 
almost be interpreted to stand for "correspondence" in the ab- 
stract. 

"Equal" does not mean in this instance the equivalence which is 
the end-in-view and the control of operations within a given 
system. For example, 7 in the series of odd integers corresponds 
to 4 in the series of all integers even and odd. The correspondence 
is genuine, as it is in the case of 9 to 5, 11 to 6, etc. While it is 
correct to say that the odd numbers in question are but a "part" 
of the "whole" set consisting of both even and odd numbers, it 
does not follow, however, that the relation between the two sets 
is that of w T hole and part in the sense in which "whole" and "part" 
relation is exemplified within the set of all integers. The succession 
of odd numbers is a part of the whole set of integers since it oc- 
curs by the very operations that determine that set. But as 
the set of odd numbers they are determined by a different opera- 
tion and as such they are not a part of the other set. Taking the 
relation as one of "whole-part" in its usual sense is like saying that 
a map of England existing in that country is a^ "part" of th; 
"whole" country, while its significant relation is that of isr 



414 THE LOGIC OF SCIENTIFIC METHOD 



morphism. That one-to-one correspondence between constitu- 
ents of the two sets should be capable of being instituted is a 
special example of transformability. The number of operations 
to be performed in ordering odd numbers is always the same as the 
number of operations involved in some number of the set of odd 
and even numbers taken together, as in the instances of 7 and 4, 
9 and 5, and so on. But in the case of 1, 2, 3, 4, etc., as parts, say, 
of 10 as a whole, although the difference between them as parts 
is a matter of integration of operations, the method of operation is 
not the same as that which discriminates the 1, 3, 5, 7 of the set of 
odd numbers. Hence these numbers are operationally different 
from the 1, 3, 5, 7 of the other set of integers. The correspond- 
ence between them (although it is not one of equivalence) can be 
regarded as that of isomorphism. As in the case noted above of 
isomorphisms generally, it institutes the possibility of a new order 
of mathematical conceptions. The category of infinity may thus be 
regarded as a formulation of correspondency in the abstract. 

I conclude this part of the discussion by reference to the mean- 
ing of "functions" in physical and mathematical inquiry respec- 
tively. When it is said that "the volume of a gas is a function of 
temperature and pressure," it is affirmed that any existential varia- 
tion in volume is correlated with variations in temperature or/and 
pressure. The formula is arrived at and tested by operations of 
experimental observation. Hence it is contingent, so that Boyles' 
formulation (cited above) was further refined to meet newly 
ascertained facts in Van't Hoff 's formulation. Given the formula- 
tion of the function, special values can be given to volume, pres- 
sure and temperature only by means of independent operations of 
existential observation. The values do not "follow" from the 
formula in the sense of being implied by them. In the case of the 
proposition y — x 2 , any operation which assigns a value to either 
x or y necessarily institutes a corresponding modification of the 
value of the other member of the equation, and the operation of 
assigning a value is determined wholly by the system of which 
the equation is a part, and is not dependent upon extra-systemic 
operations, such as those of observation. Hence the logical im- 
possibility of interpreting the form of physical generalizations 
(which are formulable as functional correlations) by carrying 



MATHEMATICAL DISCOURSE 415 

over inro thern the form of propositional and mathematical func- 
tions. 

An illustration of what is implied in the foregoing paragraphs 
may be drawn from interpretation of points and instants by the 
method of "extensive abstraction." A point in the mathematical 
sense cannot be "abstracted" in the sense of selective prescission 
from relations of physical lines, places or volumes. A point is of 
a different logical dimension from any physical area, however 
minute the matter may be. Nor is a point a mere negation of 
extension. Aside from the logical difficulties attending the merely 
negative, or negative "infinitation" in any case, the point serves 
a positive function. It is no more mere absence of extension than 
is the mere absence of number. It is a strictly relational (not 
relative) term. In the literal sense of "extensive," it cannot be 
derived by abstraction no matter how extensive. Point designates 
a relationship; and the relation^ip of enclosing-enclosed cannot be 
logically instituted by any selection out of the relations of things 
enclosed in and enclosed by one another; though this latter relation 
may suggest the abstract relationship. It bears the same relation 
to enclosed and enclosing physical volumes that fatherhood does 
to those who are fathers. The statement "A line is composed of 
points" is only a way of saying that operations of interception may 
be combined with the operation that institutes a mathematical line 
such that points are determined, while the statement "a line is 
composed of an infinite number of points" is only a way of saying 
that the complex operation in question is such that, like any opera- 
tion in this domain, it is not terminating. 

V. The Possibility of Existential Reference. It was stated at 
the outset that a logical theory of mathematics must account both 
for that absence of necessity of existential reference which renders 
mathematical propositions capable of formal certification, and for 
the generalized possibility of such reference. Up to this point 
we have been occupied with the first of these two considerations. 
The use of arithmetic in ordinary commercial transactions and 
the role of mathematics in physical science suffice to show that 
applicability is a possibility and that the possibility is actualized on 
a wide scale. Two points will be made with respect to the matter 
of possibility. 



416 THE LOGIC OF SCIENTIFIC METHOD 

1. The first point is that applicability is indefinitely compre- 
hensive precisely because of freedom from the necessity of appli- 
cation. That the range of existential applicability of mathematical 
subject-matter is in direct ratio to its abstractness is shown by the 
history of physical science in its relation to the history of mathe- 
matical science. As long as Euclidean geometry was supposed to 
have direct ontological reference, the application of geometry in 
physics was highly restricted, and when it was applied it usually 
led physics into wrong paths. Riemanian and Lobechewskian 
geometries not only freed geometry from its alleged existential 
reference (assumed not only by the ancients but by Kant in his 
theory of a connection of geometry with space and of space with 
an a priori form of conception), but in so doing it provided in- 
strumentalities for development of the physical theory of general 
relativity. Highly important developments in the special theory 
of relativity and the theory of quanta would not have been pos- 
sible without a prior independent development of branches of 
mathematics which, at the time of their origin, had, like tensor alge- 
bra and the algebra of invariants, no imaginable physical bearing. 

Such examples as these, which might be greatly multiplied, are 
not matters of coincidence. Without an idea, in itself a possi- 
bility and in so far abstract, existential transformations are brought 
about only by organic instrumentalities. The limited range of 
the activities of lower animals illustrates the result. The more 
extensive the domain of abstract conceptions and the more ex- 
tensive and abstract the operations by which they are developed 
in discourse, the more instrumentalities there are for possible ways 
of performing the physical operations which institute data as 
appropriate grounds for extensive systematic inference. How far 
these possibilities are actualized at a given time depends upon the 
state of physical knowledge at that time and particularly upon 
the physical instruments and techniques then available. But the 
possibilities are there awaiting occasion for their operative mani- 
festation. 

The Alexandrian mathematicians, it has been pointed out, had 
m their possession all the conceptions that were needed for attack 
upon problems of velocity and acceleration of motion. Hence 
theoretically they might have anticipated some of the leading 



MATHEMATICAL DISCOURSE 417 

conceptions of modern physics. 8 But Euclidean geometry exer- 
cised compulsory restrictive influence, and this influence rested 
on the supposed necessity of interpreting mathematical concep- 
tion in terms of ontological essences. The resulting restriction of 
numbers to geometrical ratios assigned specific contents to axioms 
and definitions and thereby to all theorems, so that space, time and 
motion could not be conceived in that freedom from qualitative 
considerations that is required in order to render them capable of 
free mathematical treatment, a treatment that led to an immense 
widening of application. 

2. Reference of mathematical conceptions to existence, when 
it does take place, is not direct. That reference is made by means 
of existential operations which the conceptions indicate and direct 
is a basic principle of this work. "What is here added is that in 
many cases the mathematical conceptions are instruments of di- 
rection of calculation by the results of which interpretation and 
ordering of existential data is promoted. In such cases, there is no 
direct application, even of an operative kind, to institution of data. 
Irrational numbers, for example, are not obtained by any process 
which involves only direct physical measurement. Such numbers 
are not the direct results of such operations, irrespective of whether 
these operations are conducted within the framework of concep- 
tions which involve the irrational numbers or not. Irrational 
numbers are not descriptive of the immediate outcome of opera- 
tions of measurement. But irrationals do make possible the use 
of methods of calculation whose results facilitate the ordering of 
experimental results. The same statement holds for continuous 
functions. Neither they nor irrationals permit of interpretation 
in terms of direct operational application even in those cases where 
through the medium of calculations they make possible, they enter, 
into final formulation of existential propositions. Such instances 
as these are conspicuous illustrations of the functional, non- 
descriptive, character of mathematical conceptions when used in 
natural science. They are logically significant as special evidence 

s The reference is to an essay by George H. Mead on "Scientific Method" 
in the volume Creative Intelligence. The entire passage, pp. 179-188 should be 
consulted, since it provides, as far as I am aware, the first explicit formulation of 
the connection between absence of necessary existential reference and the 
extensive possibility of such reference. 



418 THE LOGIC OF SCIENTIFIC METHOD 

of the intermediate and instrumental status of universal proposi- 
tions. Unless this interpretation is given to the results of many 
calculations, the propositions that result have to be denied validity 
because nothing corresponding to their contents can be found to 
be existential. 

The considerations here adduced have an obvious bearing upon 
the nature of test and verification (See ante, p. 157). They prove 
that in the practice of inquiry verification of an idea or theory is 
not a matter of finding an existence which answers to the demands 
of the idea or theory, but is a matter of the systematic ordering of 
a complex set of data by means of the idea or theory as an instru- 
mentality. 




CHAPTER XXI 

SCIENTIFIC METHOD: 

INDUCTION AND DEDUCTION 



- hatever else scientific method is or is not, it is con- 
cerned with ascertaining the conjunctions of charac- 
teristic traits which descriptively determine kinds in 
relation to one another and the interrelations of characters which 
constitute abstract conceptions of wide applicability. The prop- 
ositions which result are generalizations of two forms, generic and 
universal; one existential in content, the other non-existential. The 
methods by which generalizations are arrived at have received the 
name "induction"; the methods by which already existing gener- 
alizations are employed have received the name "deduction." 
These considerations at least delimit the field of discussion. Any 
account of scientific method must be capable of offering a co- 
herent doctrine of the nature of induction and deduction and of 
their relations to one another, and the doctrine must accord with 
what takes place in actual scientific practice. 

With respect to both induction and deduction, the logical ter- 
rain is still occupied with remnants, some more or less coherent 
and some more or less of the nature of debris, of logical concep- 
tions that were formed prior to the development of scientific 
method. There is, accordingly, no field of logical subject-matter 
in which the need of thoroughgoing reform of theory (the theme 
of an earlier chapter) is so urgent as in the case of induction and 
deduction. It has become traditional to repeat the statement that 
induction goes from particulars to the general and deduction from 
the general to the particulars. The extent to which these concep- 
tions are valid, i.e., in harmony with scientific practice, is not 
critically examined. The result too frequently is that actual scien- 

419 



420 THE LOGIC OF SCIENTIFIC METHOD 

tific procedure is forced into the straitjacket of irrelevant precon- 
ceptions. Escape from this procedure depends upon analysis of 
induction and deduction from the point of view of actual methods 
of inquiry. 

The traditional and still current conceptions of induction and 
deduction are derived from Aristotelian logic, which, as has been 
shown, was a systematization of logical forms on the basis of 
certain cosmological beliefs. Since the actual progress of scientific 
inquiry has led to an abandonment of these underlying beliefs con- 
cerning the structure of Nature, it might be antecedently ex- 
pected that the doctrines about induction and deduction, which 
are found in Aristotelian logic, will be so irrelevant to existing 
scientific practice as to be the source of confusion and uncertainty 
when they are employed as rubrics of interpretation. Discussion 
will not, however, be based upon this antecedent probability. I 
shall first set forth briefly the original Aristotelian doctrines in 
respect to its cosmological foundation; then give a brief summary 
of how induction and deduction are to be understood on the basis 
of logical principles already developed in this treatise, and, finally, 
present an independent analysis. 

I. Induction and Deduction in Aristotelian Logic. The concep- 
tion of induction as a procedure that goes from particulars to the 
general, and of deduction as the reverse movement, has its origin 
in the Aristotelian formulation. More important than the mere 
question of its historical derivation, is the fact that the Aristotelian 
conceptions were relevant to, and grounded in, the subject-matter 
of natural science as that subject-matter, the structure of nature, 
was then understood. There is no need at this point to expound 
at length the characteristic features of the conception of Nature 
entertained by Aristotle. The distinction between immutable Be- 
ing, existing at all times in identical form, and the mutable, which 
in its mutability is convincing proof of partial and incomplete 
Being, provided the ground of the distinction made between in- 
duction and rationally complete, scientific demonstration or de- 
duction. Since the immutable was constituted by fixed species, 
each of which was defined by an essence, it followed that strictly 
scientific or demonstrative knowledge consisted in a classificatory 
ordering of fixed species, in which inclusive species hierarchically 



INDUCTION AND DEDUCTION 421 

determined Included species of a more limited range. This order- 
ing is effected in the demonstrative syllogism. Scientific know 1- 
edge of changing things is, on the contrary, possible only when 
and as these things are caught and placed within the fixed limits 
constituted by essences that define species. The result here was 
also expressed in the syllogism, but in a contingent syllogism as 
distinct from the rational necessity of the demonstrative syl- 
logism. 1 

1. The Deductive. In each of these forms, the deductive is 
identified with the syllogistic. Given the underlying cosmological 
assumptions, there is genuine meaning in the conception of going 
from the general to the particular. In the case of the demonstra- 
tive syllogism, the movement is from the more to the less inclusive, 
where "particular" is to be understood in a strictly logical sense: — 
as equivalent to the more specific in its distinction from the uni- 
versal inclusive species. In the case of the contingent syllogism, 
"particular" has a different meaning. Anything which is mutable 
is particular in the sense of being partial, incomplete. Now the 
objects of sense perception are observed things in their severalty 
in distinction from the species to which they belong. They are, 
as just noted, truly known only when and as they are subsumed 
under universal propositions which state the inherent nature of 
species. As thus subsumed, they "follow" as particulars from the 
general. 

At this point, I shall briefly indicate the difference between 
this conception of rational demonstration and that which is In 
accord with present scientific practice. Mathematical discourse 
is now the outstanding exemplar of deductive demonstration; but 
(1) no mathematician would regard it as logically important to 
reduce a chain of related mathematical propositions to the syl- 
logistic form, nor w r ould he suppose that such reduction added 
anything to the force of his demonstrations; and (2) such deduc- 
tions do not necessarily proceed from the more general to the less 
general even with respect to conceptions; while (3) as has already 
been shown (and, indeed as is generally acknowledged), it is 

a To express the contingent nature of this form of syllogism, Aristotle fre- 
quently uses the expression "dialectic syllogisms." Their conclusions are true as 
a rule, "upon the whole," usually, but not always, since they are not derived 
from subject-matters which are themselves necessary. 



422 THE LOGIC OF SCIENTIFIC METHOD 

impossible to proceed directly from a universal proposition to one 
about an existential particular or singular. It is true (with regard 
to the second point) that sometimes in mathematical reasoning the 
final proposition has less scope or "comprehension," a narrower 
range of applicability, than do the preceding propositions from 
which it "follows." When, for example, an ellipse is defined as 
a curve so moving that its distance from a fixed line bears a con- 
stant ratio to its distance from a fixed point, the logical movement 
is from a conception of wider applicability to one restricted by 
introduction of a special limiting condition. But when the prop- 
erties of an ellipse are defined by reasoning from the properties 
of a conic section, the logical movement is from the narrower to 
the wider range of applicability. When the equilateral is derived 
from the equiangular, there is neither gain nor loss in compre- 
hension or scope. The fact is that about mathematical reasoning, 
as an example of deduction, no general statement whatever can be 
made as to the breadth of the premises in relation to that of the 
conclusion. Such differences as may be present depend upon 
the special methods used and the nature of the problem dealt with. 
So much, in general, for the irrelevancy of the Aristotelian con- 
ception of deduction to modern scientific practice. 2 

2. The Inductive. With respect to the formulation of the in- 
ductive procedures of ancient and modern science respectively 
there exists a verbal similarity. Both start from scattered data (or 
particulars) and move toward institution of generalizations. But 
the similarity does not extend beyond the vague formula of "going 
from particulars to generals." For (1) particulars are conceived 
in radically different ways and (2) the process of "going," or the 
way in which generals are arrived at from particulars, is very dif- 
ferent. The nature of inductive procedures in present day science 
is the special subject of later analysis. But, apart from the con- 
clusions of this analysis, a survey of the Aristotelian conception of 
induction suffices to show its intrinsic unfitness to serve the logical 
conditions of present science. The cosmological theory of Aris- 
totle postulates that every knowable thing is of some kind or 

2 The important difference, not touched upon in the above paragraphs, is 
that the status and force of general propositions in the classic scheme represented 
a direct notation of an inherent static structure, or essence, while in mathematics 
(as we have just seen) such propositions are operational. 



INDUCTION AND DEDUCTION 423 

species. Even sense-perception is a mode of low-grade knowledge 
in so far as what is seen, heard and touched is apprehended as being 
of a kind. The very lowest grade of knowledge, mere sensation, 
directly apprehends qualities determined by "sensible forms," such 
as, in touch, hard-soft. Sensation and sense-perception are modes 
of knowledge in which "matter," the principle of change and 
hence of lack of Being, predominates, as, e.g., when the dry changes 
to the wet. In general, the "particular" which is "known" in 
sense perception is subject to generation and dissolution, to "birth" 
and "death," as a tree grows from seed, decays and vanishes. 
Recurrent perceptions then constitute experience. I